Amount of money offered initially for wrestling (4)
I believe the answer is:
sumo
'wrestling' is the definition.
(I've seen this before)
'amount of money offered initially' is the wordplay.
'amount of money' becomes 'sum' ('sum' can be a synonym of 'amount of money'**).
'initially' suggests taking the first letters.
The first letter of 'offered' is 'o'.
'sum'+'o'='SUMO'
'for' is the link.
(Other definitions for sumo that I've seen before include "Traditional Japanese wrestling by fat men" , "Style of traditional Japanese wrestling" , "Type of Japanese wrestling" , "Jap. wrestling" , "Japanese wrestling for huge men" .)