A bit for a cat (4)
I believe the answer is:
atom
'a bit' is the definition.
(I have seen 'Tiny bit' mean 'atom' so perhaps 'bit' could also mean 'atom')
'a cat' is the wordplay.
'cat' becomes 'tom' (a tom is a male cat).
'a'+'tom'='ATOM'
'for' is the link.
(Other definitions for atom that I've seen before include "Particle of matter now divided" , "tiny thing" , "Bit of make-up" , "Particle; molecule" , "Moat (anag.)" .)