Sick have small portion under doctor — it might well be boring (5,3)
I believe the answer is:
drill bit
'it might well be boring' is the definition.
(a drill bit bores)
'sick have small portion under doctor' is the wordplay.
'sick' becomes 'ill' (synonyms).
'have' means one lot of letters go next to another.
'small portion' becomes 'bit' (I've seen this in another clue).
'under' says to put letters next to each other.
'doctor' becomes 'Dr' (abbreviation).
'ill' next to 'bit' is 'illbit'.
'illbit' after 'dr' is 'DRILL BIT'.
(Other definitions for drill bit that I've seen before include "Borer" , "tool" , "it can be boring" , "that bores" .)