Game in Los Angeles annoyed last in league (8)
I believe the answer is:
'game' is the definition.
(I've seen this before)
'los angeles annoyed last in league' is the wordplay.
'los angeles' becomes 'la'.
'annoyed' becomes 'cross' (I've seen this before).
'last in' suggests the final letters.
The final letter of 'league' is 'e'.
'la'+'cross'+'e'='LA CROSSE'
'in' acts as a link.
(Other definitions for la crosse that I've seen before include "Cor! seals can play this ball game" , "Netted-stick game" , "Game played with a netted stick" , "Game resembling hockey" , "Game played with long-handled racquets" .)