Take a chance with the better half (3)
I believe the answer is:
bet
I believe this is a double definition.
'take a chance with' is the first definition.
'better half' is the second definition.
'the' acts as a link.
(Other definitions for bet that I've seen before include "Speculation" , "'Stake, wager (3)'" , "Wager, back" , "Wager, gamble" , "22 across will accept one" .)