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