Give stress treatment to girl Alan’s chasing (6)
I believe the answer is:
anneal
'give stress treatment' is the definition.
(annealing means heating up to remove stresses)
'girl alan's chasing' is the wordplay.
'girl' becomes 'Anne' (girl's name).
'alan's chasing' becomes 'al' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'anne'+'al'='ANNEAL'
'to' is the link.
Can you help me to learn more?
(Other definitions for anneal that I've seen before include "Toughen by a process of gradually heating and cooling" , "toughening process" , "Long angry speech" , "Harden by heating and cooling" , "Heat and cool slowly to toughen, metal or glass" .)