Game giving some American a start (7)
I believe the answer is:
canasta
'game' is the definition.
(canasta is a kind of game)
'some american a start' is the wordplay.
'some' indicates the answer is hidden within the clue (some of the parts of the word are used).
'CANASTA' is hidden in the letters of 'american a start'.
'giving' is the link.
(Other definitions for canasta that I've seen before include "Form of rummy using two decks of cards and four jokers" , "Card-game played with two packs of cards" , "Card game -- as an act (anag)" , "Card game like rummy" , "Card-game, a form of rummy" .)