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' means one lot of letters goes inside another.
'bet' placed around 'a' is 'BEAT'.
(Other definitions for beat that I've seen before include "Master" , "Conquer" , "Worst - best" , "Defeat; pulsate" , "Flog" .)