Prompts me to turn in the skins (7)
I believe the answer is:
reminds
'prompts' is the definition.
('remind' can be a synonym of 'prompt')
'me to turn in the skins' is the wordplay.
'to turn' indicates anagramming the letters (letters turn into something else).
'in the' is an insertion indicator.
'skins' becomes 'rinds' ('rind' can be a synonym of 'skin').
'me' anagrammed gives 'em'.
'em' inserted within 'rinds' is 'REMINDS'.
(Other definitions for reminds that I've seen before include "Evokes a memory" , "Calls up memory" , "Prompts" .)