Live a short time with a girl (3)
I believe the answer is:
bet
'a girl' is the definition.
'live a short time' is the wordplay.
'live' becomes 'be' (synonyms).
'a short time' becomes 't' (abbreviation for time).
'be'+'t'='BET'
'with' acts as a link.
(Other definitions for bet that I've seen before include "Wager, speculate" , "'Stake, wager (3)'" , "Wager, back" , "Wager, or the sum waged" , "Speculation" .)