Bet poet's no Democrat (4)
I believe the answer is:
ante
'bet' is the definition.
(ante is a kind of bet)
'poet's no democrat' is the wordplay.
'poet' becomes 'dante' (Dante is an example).
'no' indicates named letters should be taken away.
'democrat' becomes 'd'.
'dante' with 'd' taken away is 'ANTE'.
(Other definitions for ante that I've seen before include "Preceding birth" , "Stake (that may be upped?)" , "Card-player's stake" , "Poker-player's stake before the deal" , "Player's stake in poker - a ten? (anag)" .)