Bit of a nasty eye (4)
I believe the answer is:
stye
'bit' is the definition.
Although both the answer and definition are singular nouns, I can't see how they can define each other.
'of a nasty eye' is the wordplay.
'of' says the answer is hidden in the clue.
'STYE' is hidden within 'nasty eye'.
Can you help me to learn more?
(Other definitions for stye that I've seen before include "Inflamed swelling on the edge of an eyelid" , "Eye sore" , "Climb" , "Infected swelling of the eye" , "pain for the observer" .)