Supplier of drugs quick to overcome injury (8)
I believe the answer is:
pharmacy
'supplier of drugs' is the definition.
(a pharmacy supplies drugs)
'quick to overcome injury' is the wordplay.
'quick' becomes 'pacy'.
'to overcome' means one lot of letters goes inside another (some letters come over or go around others).
'injury' becomes 'harm' (synonyms).
'pacy' enclosing 'harm' is 'PHARMACY'.
(Other definitions for pharmacy that I've seen before include "Drug store" , "Where drugs are dispensed" , "Medical establishment" , "Place where drugs are prepared or sold" , "Where chemist works" .)