Comatose pet needing a pick-me-up? (9)
I believe the answer is:
catatonic
'comatose' is the definition.
(thesaurus)
'pet needing a pick-me-up?' is the wordplay.
'pet' becomes 'cat' (cats are often kept as pets).
'needing' says to put letters next to each other.
'pick-me-up?' becomes 'tonic' (pick-me-up is a kind of tonic).
'cat'+'a'+'tonic'='CATATONIC'
(Other definitions for catatonic that I've seen before include "Rigid and in a stupor through illness" , "Having muscular rigidity and stupor" , "In a state of stupor - cat in coat (anag)" , "Unable to move" , "In a stupefied state" .)