Put the right first name in but was fired (5)
I believe the answer is:
burnt
'fired' is the definition.
(I've seen this in another clue)
'put the right first name in but' is the wordplay.
'put' indicates putting letters inside.
'the right' becomes 'r' (abbreviation).
'first name' becomes 'n' (1st letter of 'name').
'in' indicates putting letters inside.
'n' going into 'but' is 'bunt'.
'r' placed into 'bunt' is 'BURNT'.
'was' acts as a link.
(Other definitions for burnt that I've seen before include "Ruined by overcooking" , "Affected by fire" , "Incinerated" , "one sent to stake" , "Destroyed by fire" .)