Hair application allergy not oddly brought up (3)
I believe the answer is:
gel
'hair application' is the definition.
Although both the answer and definition are singular nouns, I cannot see how they can define each other.
'allergy not oddly brought up' is the wordplay.
'not oddly' indicates alternate letters (odd letters are removed).
'brought up' shows that the letters should be reversed in order (down clues only).
The alternating letters of 'allergy' are 'leg'.
'leg' in reverse letter order is 'GEL'.
Can you help me to learn more?
(Other definitions for gel that I've seen before include "Leg it and get it for your hair, say" , "Hair cosmetic" , "Colloid" , "Capital preparation" , "Become jelly-like" .)