Extremely awkward teacher reveals accessory (3-2)
I believe the answer is:
add-on
'accessory' is the definition.
(I've seen this in another clue)
'extremely awkward teacher' is the wordplay.
'extremely' suggests removing the centre (only the extremes of the word are used).
'teacher' becomes 'don' (don can mean an academic - especially at Oxbridge).
'awkward' with its centre taken out is 'ad'.
'ad'+'don'='ADD-ON'
'reveals' is the link.
(Other definitions for add-on that I've seen before include "Extra bit" , "Computer peripheral" , "Optional item as supplement or increment" , "Extra unit, peripheral" , "Extra charge" .)