Membrane at eardrum being damaged (4,5)

I believe the answer is:

dura mater

'membrane' is the definition.
(dura mater is a kind of membrane)

'at eardrum being damaged' is the wordplay.
'being damaged' indicates anagramming the letters.
'at'+'eardrum'='ateardrum'
'ateardrum' with letters rearranged gives 'DURA MATER'.

(Another definition for dura mater that I've seen is " membrane".)

I've seen this clue in The Telegraph.

Want a hint initially instead of a full solution? Install my app