Frail food store pet beginning to eat (8)
I believe the answer is:
delicate
'frail' is the definition.
(synonyms)
'food store pet beginning to eat' is the wordplay.
'food store' becomes 'deli' (I've seen this in other clues).
'pet' becomes 'cat' (I have seen 'Common pet ' mean 'cat' so perhaps 'pet' could also mean 'cat').
'beginning to' says to take the initial letters.
The initial letter of 'eat' is 'e'.
'deli'+'cat'+'e'='DELICATE'
(Other definitions for delicate that I've seen before include "Very fine in structure" , "Soft" , "Very fine or easily broken" , "Not strong or healthy" , "Dainty - fragile" .)