Wager has a pulse (4)
I believe the answer is:
beat
'pulse' is the definition.
(synonyms)
'wager has a' is the wordplay.
'wager' becomes 'bet' (synonyms).
'has' indicates putting letters inside.
'bet' placed around 'a' is 'BEAT'.
(Other definitions for beat that I've seen before include "Master" , "Conquer" , "Worst - best" , "Defeat; pulsate" , "Flog" .)