Jet fighter almost precipitated a headache (8)
I believe the answer is:
migraine
'a headache' is the definition.
(migraine is a kind of headache)
'jet fighter almost precipitated' is the wordplay.
'jet fighter' becomes 'mig' (I've seen this in other clues).
'almost' means to remove the last letter (most of the word but not all of it).
'precipitated' becomes 'rained' (raining is a kind of precipitating).
'rained' with its final letter taken away is 'raine'.
'mig'+'raine'='MIGRAINE'
(Other definitions for migraine that I've seen before include "attack" , "Recurrent throbbing headache" , "From mare gin I get a severe headache" , "Throbbing inside the head" , "Long nerve fibre" .)