Got to fly: inspector’s outside at the front! (5)
I believe the answer is:
irked
'got to' is the definition.
(to get to someone is to annoy or irk them)
'fly inspector's outside at the front' is the wordplay.
'fly' becomes 'ked' (type of insect).
'outside' means to remove the middle letters.
'at the front' is a charade indicator (letters next to each other).
'inspector' with its middle taken out is 'ir'.
'ked' after 'ir' is 'IRKED'.
(Other definitions for irked that I've seen before include "Galled" , "Exasperated" , "Bugged" , "Wound" , "disgusted" .)