Is outwardly relieved but didn't give in (8)
I believe the answer is:
resisted
'didn't give in' is the definition.
I can't judge whether this defines the answer.
'is outwardly relieved' is the wordplay.
'outwardly' means one lot of letters goes inside another (some letters go outside others).
'relieved' becomes 'rested' (I can't explain this - if you can you should believe this answer much more).
'is' inserted into 'rested' is 'RESISTED'.
'but' is the link.
Can you help me to learn more?
(Other definitions for resisted that I've seen before include "Put up opposition from editress" , "Refused to give in" , "Struggled against" , "Withstood a force" , "Defied" .)