For example, a toothbrush might initially get rid of persistent pain (9)
I believe the answer is:
moustache
'for example a toothbrush' is the definition.
I can't tell whether this definition defines the answer.
'might initially get rid of persistent pain' is the wordplay.
'initially' suggests taking the first letters.
'get rid of' becomes 'oust' (I've seen this before).
'persistent pain' becomes 'ache' (I've seen this before).
The first letter of 'might' is 'm'.
'm'+'oust'+'ache'='MOUSTACHE'
Can you help me to learn more?
(Other definitions for moustache that I've seen before include "Facial hair growth" , "something hairy" , "Facial adornment" , "See 1" , "Food trap" .)