The money was despatched, I hear (4)
I believe the answer is:
cent
'the money' is the definition.
(eg denomination of dollars)
'despatched i hear' is the wordplay.
'despatched' becomes 'sent' (to despatch is to send off).
'i hear' shows a homophone (sound like).
'sent' is a homophone of 'CENT'.
'was' is the link.
(Other definitions for cent that I've seen before include "1/100 of various currencies" , "One-hundredth of the value of the basic unit" , "Part of a dollar" , "Small amount of money" , "Small change" .)