Given money each year — one dollar, initially (4)
I believe the answer is:
paid
'given money' is the definition.
(to give someone money is to pay them)
'each year one dollar initially' is the wordplay.
'each year' becomes 'PA' (abbreviation for per annum).
'one' becomes 'I' (Roman numeral).
'initially' says to take the initial letters.
The first letter of 'dollar' is 'd'.
'pa'+'i'+'d'='PAID'
(Other definitions for paid that I've seen before include "Settled debt" , "Forked out" , "Handed over money" , "Trite phrase" , "Aggressive, rowdy" .)