Disease got from hair on rabbit (7)
I believe the answer is:
lockjaw
'disease' is the definition.
(lockjaw is a kind of health problem)
'hair on rabbit' is the wordplay.
'hair' becomes 'lock' (lock is a kind of hair).
'on' is a charade indicator (letters next to each other).
'rabbit' becomes 'jaw'.
'lock'+'jaw'='LOCKJAW'
'got from' acts as a link.
(Other definitions for lockjaw that I've seen before include "disease resulting" , "Form of tetanus in which mouth is tightly closed" , "Form of tetanus with rigidly closed mouth" , "trap closer" , "Serious condition" .)