Cat sees bats about one in the morning (7)
I believe the answer is:
siamese
'cat' is the definition.
(I know that Siamese is a type of cat)
'sees bats about one in the morning' is the wordplay.
'bats' is an anagram indicator (slang for mad).
'about' is an insertion indicator.
'one in the morning' becomes 'Iam' (1am).
'sees' anagrammed gives 'sese'.
'sese' going around 'iam' is 'SIAMESE'.
(Other definitions for siamese that I've seen before include "Pale breed of cat" , "type of cat" , "Cat - Thai?" , "Cat with slanting blue eyes and pale fur with darker points" , "like a cat" .)