Encourage American gamble (4)
I believe the answer is:
abet
'encourage' is the definition.
(I've seen this before)
'american gamble' is the wordplay.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'gamble' becomes 'bet' (betting is a kind of gambling).
'a'+'bet'='ABET'
(Other definitions for abet that I've seen before include "Incite, help" , "Aid as in committing crime" , "Help to do something wrong" , "Assist (in doing wrong?)" , "Assist illegally" .)