It's boring for a doctor being unwell (5)
I believe the answer is:
drill
'it's boring' is the definition.
(I've seen this in another clue)
'doctor being unwell' is the wordplay.
'doctor' becomes 'dr' (abbreviation).
'being unwell' becomes 'ill' ('ill' can be similar in meaning to 'unwell').
'dr'+'ill'='DRILL'
'for a' acts as a link.
(Other definitions for drill that I've seen before include "Rehearsal; boring tool" , "Stout cotton cloth" , "training exercise" , "Routine" , "Training (to make holes?)" .)