Perhaps bills of swans seen in river (7)
I believe the answer is:
expense
'perhaps bills' is the definition.
(I know that invoice is a type of expense)
'swans seen in river' is the wordplay.
'swans' becomes 'pens' (pen is a kind of swan).
'seen in' indicates putting letters inside.
'river' becomes 'exe' (River Exe).
'pens' placed into 'exe' is 'EXPENSE'.
'of' is the link.
(Other definitions for expense that I've seen before include "Charge" , "What something costs" , "Money spent in the course of work" , "Incurred cost" , "Disbursement" .)