One King George invading American state becomes a headache (8)
I believe the answer is:
migraine
'a headache' is the definition.
(migraine is a kind of headache)
'one king george invading american state' is the wordplay.
'one' becomes 'i' (Roman numeral).
'king george' becomes 'gr' (Georgius Rex).
'invading' indicates putting letters inside.
'american state' becomes 'maine' (Maine is an example).
'i'+'gr'='igr'
'igr' inserted into 'maine' is 'MIGRAINE'.
'becomes' is the link.
(Other definitions for migraine that I've seen before include "Sick headache" , "Thumping headache" , "Severe headache often accompanied by nausea" , "A really nasty headache" , "may give one a sort of headache" .)