Some teachers could be a pain in the neck (4)
I believe the answer is:
ache
'a pain in the neck' is the definition.
(I've seen this in another clue)
'some teachers could' is the wordplay.
'some' indicates the answer is hidden within the clue (some of the parts of the word are used).
'ACHE' is hidden in the letters of 'teachers could'.
'be' is the link.
(Other definitions for ache that I've seen before include "Shakespearean character" , "Longing" , "yearning" , "burn" , "Each (anag.)" .)