Cat sees bats about one in the morning (7)
I believe the answer is:
siamese
'cat' is the definition.
(Siamese is an example)
'sees bats about one in the morning' is the wordplay.
'bats' indicates anagramming the letters (slang for mad).
'about' means one lot of letters goes inside another.
'one in the morning' becomes 'Iam' (1am).
'sees' anagrammed gives 'sese'.
'sese' enclosing '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" .)