Weary of being drilled (5)
I believe the answer is:
bored
I believe this is a double definition.
'weary' is the first definition.
(thesaurus)
'being drilled' is the second definition.
(I've seen this before)
'of' acts as a link.
(Other definitions for bored that I've seen before include "Filled with ennui" , "Extremely uninterested" , "Palled on" , "Feeling weary and uninterested" , "Robed (anag.)" .)