Initially brassed off with students getting extra money (5)
I believe the answer is:
bonus
'extra money' is the definition.
(I've seen this before)
'initially brassed off with students' is the wordplay.
'initially' says to take the initial letters.
'with' means one lot of letters go next to another.
'students' becomes 'nus' (I've seen this in other clues).
The initial letters of 'brassed off' is 'bo'.
'bo'+'nus'='BONUS'
'getting' acts as a link.
(Other definitions for bonus that I've seen before include "Additional payment as reward for service" , "Good-performance payment" , "- generis means unique" , "Additional award" , "Payment additional to the expected or usual" .)