The Jarlier Drop

While riding a hippogriff this is how you can grab and drop an enemy.

1. Must be next to the enemy. Vertically or horizontally. 
2. Grapple check to grab the enemy. A Strength (Athletics) check (+3 for hippogriff) contested by the target’s Strength (Athletics) or Dexterity (Acrobatics) check. The target chooses the ability to use. (1 action) 
3. Use any remaining movement to fly up. (max 60ft flight movement for Hippogriff) 
4. The enemy can be dropped at any time. 
5. Enemy takes 1d6 bludgeoning damage for every 10 feet it fell, to a maximum of 20d6. The creature lands prone, unless it avoids taking damage from the fall. 

If the enemy is still grappled, the hippogriff/player can fly higher.

If the enemy is grappled on their turn, they can break the gapple by making a Strength (Athletics) or Dexterity (Acrobatics) check as contested by the Hippogriff's Strength (Athletics) check, +3.