Stroll to make a wager, losing head (5)
I believe the answer is:
amble
'stroll' is the definition.
(synonyms)
'a wager losing head' is the wordplay.
'a wager' becomes 'gamble' (I've seen this before).
'losing head' means to remove the first letter.
'gamble' with its first letter taken away is 'AMBLE'.
'to make' acts as a link.
(Other definitions for amble that I've seen before include "Casual walk" , "Toddler does this" , "Walk gently" , "promenade" , "Dawdle" .)