The description of the grease spell states:
A creature that enters the area or ends its turn there must also succeed on a Dexterity saving throw or fall prone.
What about a creature that enters the area and ends its turn there? That is, if a creature enters the area and succeeds at its save (or fails, falls down, and uses its remaining movement to stand up again), then remains in the greased area, does it have to make another save at the end of its turn?
Yes, Grease can trigger multiple saves
The description text for Grease states:
A saving throw is triggered under three conditions:
There are no limitations on the number of saves the creature makes per turn/round. It's possible to force even more saves with clever play.
Spells that don't require additional saves due to movement, such as Moonbeam, state:
Grease does not contain this text and can trigger multiple saves.