A cat had a very tiny bit (4)
I believe the answer is:
atom
'tiny bit' is the definition.
(I've seen this in another clue)
'a cat' is the wordplay.
'cat' becomes 'tom' (a tom is a male cat).
'a'+'tom'='ATOM'
'had a very' is the link.
This may not be correct. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for atom that I've seen before include "Small particle of matter" , "An explosive particle as in bomb" , "Smallest particle in an element able to take part in a chemical reaction" , "Something very small perhaps" , "Scrap" .)