Cat briefly comes back to eat or drink (3)
I believe the answer is:
sup
'eat or drink' is the definition.
(to sup is to take food or drink)
'cat briefly comes back' is the wordplay.
'cat' becomes 'puss' (puss is a kind of cat).
'briefly' means to remove the last letter.
'comes back' says the letters should be written in reverse.
'puss' with its final letter taken away is 'pus'.
'pus' reversed gives 'SUP'.
'to' is the link.
(Other definitions for sup that I've seen before include "Imbibe" , "Drink; eat evening meal" , "Drink; take an evening meal" , "Take food" , "Drink; take a late meal" .)