Ape or alligator not at play (7)
I believe the answer is:
gorilla
'ape' is the definition.
(gorilla is a kind of ape)
'alligator not at play' is the wordplay.
'not' indicates named letters should be taken away.
'play' is an anagram indicator.
'alligator' with 'at' removed is 'alligor'.
'alligor' with letters rearranged gives 'GORILLA'.
'or' is the link.
(Other definitions for gorilla that I've seen before include "Large animal" , "A large powerful African ape" , "Powerful great ape" , "The biggest ape" , "Primate - sturdily-built aggressive man" .)