Quick to admit each trouncing (6)
I believe the answer is:
defeat
'trouncing' is the definition.
(thesaurus)
'quick to admit each' is the wordplay.
'quick' becomes 'deft' (I've seen this in another clue).
'to admit' means one lot of letters goes inside another.
'each' becomes 'ea' (abbreviation).
'deft' placed around 'ea' is 'DEFEAT'.
(Other definitions for defeat that I've seen before include "failure" , "best or worst" , "Vanquish, win against" , "Overthrow" , "Conquer" .)