Something used by dentist or doctor badly (5)
I believe the answer is:
drill
'something used by dentist' is the definition.
I can't judge whether this definition defines the answer.
'doctor badly' is the wordplay.
'doctor' becomes 'dr' (abbreviation).
'badly' becomes 'i'll' ('ill' can be adverbial as in 'ill-advised').
'dr'+'ill'='DRILL'
'or' is the link.
Can you help me to learn more?
(Other definitions for drill that I've seen before include "Make a hole with a pointed tool" , "Train (by repeated practice)" , "Tool, instruction" , "Procedure - practice" , "Exercise or teach through repeated practice" .)