Keen, say, to vary bets (7)
I believe the answer is:
yankees
'bets' is the definition.
(I have seen 'multiple bets' mean 'yankees' so perhaps 'bets' could also mean 'yankees')
'keen say to vary' is the wordplay.
'to vary' indicates anagramming the letters.
'keen'+'say'='keensay'
'keensay' is an anagram of 'YANKEES'.
(Other definitions for yankees that I've seen before include "Union troops" , "Side in US Civil War" , "New York baseball team" , "Americans who fought for the north in civil war" , "Code words on the radio for US" .)