Unresponsive pet given a pick-me-up (9)
I believe the answer is:
catatonic
'unresponsive' is the definition.
(I've seen this before)
'pet given a pick-me-up' is the wordplay.
'pet' becomes 'cat' (cats are often kept as pets).
'given' is a charade indicator (letters next to each other).
'pick-me-up' becomes 'tonic' (I've seen this in another clue).
'cat'+'a'+'tonic'='CATATONIC'
(Other definitions for catatonic that I've seen before include "Senseless, not moving" , "Stupefied and immobile" , "In an immobile stupor" , "unresponsive" , "In a stupefied state" .)