If one creature wants to jump onto another creature, it can do so by grappling. A Small or Medium creature has little chance of making a successful grapple against a Huge or Gargantuan creature, however, unless magic has granted the grappler supernatural might.
As an alternative, a suitably large opponent can be treated as terrain for the purpose of jumping onto its back or clinging to a limb. After making any ability checks necessary to get into position and onto the larger creature, the smaller creature uses its action to make a Strength (Athletics) or Dexterity (Acrobatics) check contested by the target's Dexterity (Acrobatics) check. If it wins the contest, the smaller creature successfully moves into the target creature's space and clings to its body. While in the target's space, the smaller creature moves with the target and has advantage on attack rolls against it.
The smaller creature can move around within the larger creature's space, treating the space as difficult terrain. The larger creature's ability to attack the smaller creature depends on the smaller creature's location, and is left to your discretion. The larger creature can dislodge the smaller creature as an action—knocking it
off, scraping it against a wall, or grabbing and throwing it—by making a Strength (Athletics) check contested by the smaller creature's Strength (Athletics) or Dexterity (Acrobatics) check. The smaller creature chooses which ability to use.
DMG Chapter 9 Combat Options
A creature can use a weapon attack to knock a weapon or another item from a target's grasp. The attacker makes an attack roll contested by the target's Strength (Athletics) check or Dexterity (Acrobatics) check. If the attacker wins the contest, the attack causes no damage or other ill effect, but the defender drops the item.
The attacker has disadvantage on its attack roll if the target is holding the item with two or more hands. The target has advantage on its ability check if it is larger than the attacking creature, or disadvantage if it is smaller.
DMG Chapter 9 Combat Options
This option makes it easier for melee combatants to harry each other with opportunity attacks.
When a creature makes a melee attack, it can also mark its target. Until the end of the attacker's next turn, any opportunity attack it makes against the marked target has advantage. The opportunity attack doesn't expend the attacker's reaction, but the attacker can't make the attack if anything, such as the incapacitated condition or the shocking grasp spell, is preventing it from taking reactions. The attacker is limited to one opportunity attack per turn.
DMG Chapter 9 Combat Options
When a creature tries to move through a hostile creature's space, the mover can try to force its way through by overrunning the hostile creature. As an action or a bonus action, the mover makes a Strength (Athletics) check contested by the hostile creature's Strength (Athletics) check. The creature attempting the overrun has advantage on this check if it is larger than the hostile creature, or disadvantage if it is smaller. If the mover wins the contest, it can move through the hostile creature's space once this turn.
DMG Chapter 9 Combat Options
Using the Attack action, you can make a Special melee Attack to shove a creature, either to knock it prone or push it away from you. If you're able to make multiple attacks with the Attack action, this Attack replaces one of them.
The target must be no more than one size larger than you and must be within your reach. Instead of Making an Attack roll, you make a Strength (Athletics) check contested by the target's Strength (Athletics) or Dexterity (Acrobatics) check (the target chooses the ability to use). If you win the contest, you either knock the target prone or push it 5 feet away from you.
https://roll20.net/compendium/dnd5e/Combat
Shove Aside Option:
With this option, a creature uses the special shove attack from the Player's Handbook to force a target to the side, rather than away. The attacker has disadvantage on its Strength (Athletics) check when it does so. If that check is successful, the attacker moves the target 5 feet to a different space within its reach.
DMG Chapter 9 Combat Options
A creature can try to tumble through a hostile creature's space, ducking and weaving past the opponent. As an action or a bonus action, the tumbler makes a Dexterity (Acrobatics) check contested by the hostile creature's Dexterity (Acrobatics) check. If the tumbler wins the contest, it can move through the hostile creature's space once this turn.
DMG Chapter 9 Combat Options
Walls, trees, creatures, and other obstacles can provide cover during combat, making a target more difficult to harm. A target can benefit from cover only when an Attack or other Effect originates on the opposite side of the cover.
There are three degrees of cover. If a target is behind multiple sources of cover, only the most protective degree of cover applies, the degrees aren't added together. For example, if a target is behind a creature that gives half cover and a tree trunk that gives three--quarters cover, the target has three--quarters cover.
A target with half cover has a +2 bonus to AC and Dexterity Saving Throws. A target has half cover if an obstacle blocks at least half of its body. The obstacle might be a low wall, a large piece of furniture, a narrow tree trunk, or a creature, whether that creature is an enemy or a friend.
A target with three--quarters cover has a +5 bonus to AC and Dexterity Saving Throws. A target has three--quarters cover if about three--quarters of it is covered by an obstacle. The obstacle might be a portcullis, an arrow slit, or a thick tree trunk.
A target with total cover can't be targeted directly by an Attack or a spell, although some Spells can
reach such a target by including it in an area of Effect. A target has total cover if it is completely concealed by an obstacle.
https://roll20.net/compendium/dnd5e/Combat
Hitting Cover DMG Option:
When a ranged attack misses a target that has cover, you can use this optional rule to determine whether the cover was struck by the attack.
First, determine whether the attack roll would have hit the protected target without the cover. If the attack roll falls within a range low enough to miss the target but high enough to strike the target if there had been no cover, the object used for cover is struck. If a creature is providing cover for the missed creature and the attack roll exceeds the AC of the covering creature, the covering creature is hit.
DMG Chapter 9 Combat Options
Your Strength (Athletics) check covers difficult situations you encounter while climbing, jumping, or swimming. Examples include the following activities:
• You attempt to climb a sheer or slippery cliff, avoid hazards while scaling a wall, or cling to a surface while something is trying to knock you off.
• You try to jump an unusually long distance or pull off a stunt midjump.
• You struggle to swim or stay afloat in treacherous currents, storm-tossed waves, or areas of thick seaweed. Or another creature tries to push or pull you underwater or otherwise interfere with your swimming.
https://www.dndbeyond.com/sources/basic-rules/using-ability-scores#AbilityChecks
Variant: Skills with Different Abilities
Normally, your proficiency in a skill applies only to a specific kind of ability check. Proficiency in Athletics, for example, usually applies to Strength checks. In some situations, though, your proficiency might reasonably apply to a different kind of check. In such cases, the DM might ask for a check using an unusual combination of ability and skill, or you might ask your DM if you can apply a proficiency to a different check. For example, if you have to swim
from an offshore island to the mainland, your DM might call for a Constitution check to see if you have the stamina to make it that far. In this case, your DM might allow you to apply your proficiency in Athletics and ask for a Constitution (Athletics) check. So if you're proficient in Athletics, you apply your proficiency bonus to the Constitution check just as you would normally do for a Strength (Athletics) check...
Notes:
In addition to the rules above, references to Athletics can also be found in rules sections covering Grappling and Shoving.
When you attempt to influence someone through overt threats, hostile actions, and physical violence, the DM might ask you to make a Charisma (Intimidation) check. Examples include trying to pry information out of a prisoner, convincing street thugs to back down from a confrontation, or using the edge of a broken bottle to convince a sneering vizier to reconsider a decision.
https://www.dndbeyond.com/sources/basic-rules/using-ability-scores#AbilityChecks
Variant: Skills with Different Abilities
Normally, your proficiency in a skill applies only to a specific kind of ability check. For example, when your half-orc barbarian uses a display of raw strength to intimidate an enemy, your DM might ask for a Strength (Intimidation) check, even though Intimidation is normally associated with Charisma.
Your Strength determines how far you can jump.
Long Jump. When you make a long jump, you cover a number of feet up to your Strength score if you move at least 10 feet on foot immediately before the jump. When you make a standing long jump, you can leap only half that distance. Either way, each foot you clear on the jump costs a foot of movement.
This rule assumes that the height of your jump doesn't matter, such as a jump across a stream or chasm. At your DM's option, you must succeed on a DC 10 Strength (Athletics) check to clear a low obstacle (no taller than a quarter of the jump's distance), such as a hedge or low wall. Otherwise, you hit it.
When you land in difficult terrain, you must succeed on a DC 10 Dexterity (Acrobatics) check to land on your feet. Otherwise, you land prone.
High Jump. When you make a high jump, you leap into the air a number of feet equal to 3 + your Strength modifier (minimum of 0 feet) if you move at least 10 feet on foot immediately before the jump. When you make a standing high jump, you can jump only half that distance. Either way, each foot you clear on the jump costs a foot of movement. In some circumstances, your DM might allow you to
make a Strength (Athletics) check to jump higher than you normally can.
You can extend your arms half your height above yourself during the jump. Thus, you can reach above you a distance equal to the height of the jump plus 1 1/2 times your height.
Each foot of movement costs 1 extra foot (2 extra feet in difficult terrain) when you’re climbing, swimming, or crawling. You ignore this extra cost if you have a climbing speed and use it to climb or a swimming speed and use it to swim. At the DM’s option, climbing a slippery vertical surface or one with few handholds requires a successful Strength (Athletics) check. Similarly, gaining any distance in rough water might require a successful Strength (Athletics) check.