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' placed around 'me' is 'WARMED'.
'and' is the link.
Can you help me to learn more?
(Other definitions for warmed that I've seen before include "gave enthusiasm" , "given thermal treatment" , "Heated" .)