Determination and spirit after first of defeats — one's beaten (5,4)
I believe the answer is:
steel drum
'one's beaten' is the definition.
(a steal drum is beaten)
'determination and spirit after first of defeats' is the wordplay.
'determination' becomes 'steel' (steel can figuratively mean determination).
'and' is a charade indicator (letters next to each other).
'spirit' becomes 'rum' (alcoholic spirit).
'after' means one lot of letters go next to another.
'first of defeats' becomes 'd' (1st letter of 'defeats').
'rum' after 'd' is 'drum'.
'steel' next to 'drum' is 'STEEL DRUM'.
(Other definitions for steel drum that I've seen before include "Metal instrument" , "Trinidadian instrument" .)