The protege accepted me and started to like me better (6)
I believe the answer is:
warmed
'started to like me better' is the definition.
I can't judge whether this defines the answer.
'the protege accepted me' is the wordplay.
'the protege' becomes 'ward' (both can mean a child in someone's care).
'accepted' means one lot of letters goes inside another.
'ward' enclosing 'me' is 'WARMED'.
'and' acts as a link.
Can you help me to learn more?
(Other definitions for warmed that I've seen before include "gave enthusiasm" , "given thermal treatment" , "Heated" .)