Bitter quarrel initially talked about after surgeon pockets tip (8)
I believe the answer is:
vendetta
'bitter quarrel' is the definition.
(a vendetta is a feud)
'initially talked about after surgeon pockets tip' is the wordplay.
I cannot really understand how this works, but
'about' could be 'a' (abbreviation in Chambers) and 'a' is found in the answer.
'tip' could be 'end' (tip can mean the end of something) and 'end' is located in the answer.
'surgeon' could be 'vet' (I've seen this in other clues) and 'vet' is found in the remaining letters.
A single letter 't' remains which might be clued in a way I don't understand.
This explanation may well be incorrect...
(Other definitions for vendetta that I've seen before include "Private feud" , "ongoing row" , "ding-dong battle" , "Unremitting battle" , "rivalry" .)