Grovelling son, possibly prodigal (7)
I believe the answer is:
slavish
'grovelling' is the definition.
(thesaurus)
'son possibly prodigal' is the wordplay.
I cannot really understand how this works, but
'son' could be 's' (genealogical abbreviation for son) and 's' is present in the answer.
'prodigal' could be 'lavish' (similar in meaning) and 'lavish' is present in the answer.
This accounts for all the letters.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for slavish that I've seen before include "fawning" , "Unoriginal" , "Submissive, servile" , "that's hardly original" , "laborious" .)