Girl going to West London district for toughening (9)
I believe the answer is:
annealing
'toughening' is the definition.
(annealing is a kind of toughening)
'girl going to west london district' is the wordplay.
'girl' becomes 'ann' (woman's name).
'going to' says to put letters next to each other.
'west london district' becomes 'ealing' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'ann'+'ealing'='ANNEALING'
'for' acts as a link.
Can you help me to learn more?
(Other definitions for annealing that I've seen before include "Working to de-stress" , "Making tough" , "getting tough" , "Relieving internal stresses by heating and cooling" , "toughening" .)