Fire displayed by sports nut (5)
I believe the answer is:
pecan
'nut' is the definition.
(type of nut)
'fire displayed by sports' is the wordplay.
'fire' becomes 'can' (dismiss from job).
'displayed by' is a charade indicator (letters next to each other).
'sports' becomes 'pe' (Physical Education).
'can' put after 'pe' is 'PECAN'.
(Other definitions for pecan that I've seen before include "Oval nut of south central United States" , "Type of nut" , "Nut tree of the southern United States and Mexico" , "Pinkish-brown nut used in American pie" , "Something like a walnut" .)