Demanded payment to construct, say (6)
I believe the answer is:
billed
'demanded payment' is the definition.
('bill' can be a synonym of 'demand payment')
'construct say' is the wordplay.
'construct' becomes 'build' ('build' can be a synonym of 'construct').
'say' indicates a 'sounds like' (homophone) clue.
'build' is a homophone of 'BILLED'.
'to' is the link.
(Other definitions for billed that I've seen before include "Sent an invoice" , "Listed in a programme; charged" , "Caressed" , "Advertised" .)