I’ll be taking no flights? Rising anger after heading out (3)
I believe the answer is:
emu
'i'll be taking no flights?' is the definition.
(emu is a flightless bird)
'rising anger after heading out' is the wordplay.
'rising' is a reversal indicator (going up in a down clue).
'anger' becomes 'fume' (as in the phrase 'in a fume').
'after heading out' means to remove the first letter.
'fume' with its first letter removed is 'ume'.
'ume' reversed gives 'EMU'.
(Other definitions for emu that I've seen before include "it'll never fly!" , "Australian non-flyer" , "Flightless bird of Australia, like ostrich" , "Fast runner in Oz" , "that doesn't get off the ground" .)