Remaining ill, ignoring a new headache (8)
I believe the answer is:
migraine
'headache' is the definition.
(migraine is a kind of headache)
I don't understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for migraine that I've seen before include "Recurrent throbbing headache" , "Disabling headache" , "Severe headache often accompanied by nausea" , "may give one a sort of headache" , "Severe recurrent headache" .)