Moderate girl backed by terse extremists (9)
I believe the answer is:
alleviate
'moderate' is the definition.
(I've seen this in another clue)
'girl backed by terse extremists' is the wordplay.
I cannot really understand how this works, but
'girl' could be 'vi' (short for Violet) and 'vi' is present in the answer.
'by' could be 'at' and 'at' is present in the answer.
The remaining letters 'allee' is a valid word which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for alleviate that I've seen before include "Make better" , "Make (suffering etc) easier to bear" , "To mollify" , "moderate" , "Make less severe as with pain" .)