Parent finally had tea cooked (3)
I believe the answer is:
dad
'parent' is the definition.
(dad can informally mean father)
'finally had tea cooked' is the wordplay.
'finally' indicates one should take the final letters.
The last letters of 'had tea cooked' are 'DAD'.
(Other definitions for dad that I've seen before include "Mum's mate" , "Popular and informal father" , "Old man" , "Relation" , "Father, in short" .)