Needle game's inconclusive (5)
I believe the answer is:
pique
'needle' is the definition.
(both can mean to annoy)
'game's inconclusive' is the wordplay.
'game' becomes 'piquet' (piquet is a kind of game).
'inconclusive' means to remove the last letter.
'piquet' with its last letter taken away is 'PIQUE'.
(Other definitions for pique that I've seen before include "Feeling of resentment or indignation" , "Nettle" , "Hurt feelings" , "Angry resentment" , "Ill-feeling; fabric" .)