Struggled rather to concede first lost game (10)
I believe the answer is:
battledore
'game' is the definition.
(battledore is a kind of game)
'struggled rather' is the wordplay.
'struggled' becomes 'battled' (battling is a kind of struggling).
'rather' becomes 'ore' (I can't justify this - if you can you should give a lot more credence to this answer).
'battled'+'ore'='BATTLEDORE'
'to concede first lost' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for battledore that I've seen before include "game" , "Not much of a racket" , "Forerunner of Badminton" .)