Auctioneer initially increases sums (7)
I believe the answer is:
amounts
'sums' is the definition.
('amount' can be a synonym of 'sum')
'auctioneer initially increases' is the wordplay.
'initially' suggests taking the first letters.
'increases' becomes 'mounts' (mounting is a kind of increasing).
The first letter of 'auctioneer' is 'a'.
'a'+'mounts'='AMOUNTS'
(Other definitions for amounts that I've seen before include "Total numbers or quantities" , "Totals, sums" , "Supplies" , "Measures" .)