Increase in US money swamps rock group (9)
I believe the answer is:
increment
'increase' is the definition.
(I know that increase can be written as increment)
'in us money swamps rock group' is the wordplay.
'us money' becomes 'cent' (US coin).
'swamps' indicates putting letters inside (inserted letters are covered up or swamped).
'rock group' becomes 'REM' (REM are a US rock band).
'cent' going around 'rem' is 'crement'.
'in'+'crement'='INCREMENT'
(Other definitions for increment that I've seen before include "growth" , "Small change" , "Step" , "Amount by which something increases" , "additional pay" .)