Drilled but was reduced to a state of tedium (5)
I believe the answer is:
bored
'drilled' is the definition.
('bore' can be a synonym of 'drill')
'was reduced to a state of tedium' is the wordplay.
I cannot really see how this works, but
'state' could be 'or' and 'or' is found within the answer.
The remaining letters 'bed' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...
'but' is the link.
Can you help me to learn more?
(Other definitions for bored that I've seen before include "Tired and uninterested" , "Lacking stimulation" , "Wearied by tedium" , "Used drill on" , "Drilled; wearied" .)