New peer's given ring portraying Zeus's daughter (10)
I believe the answer is:
persephone
'zeus's daughter' is the definition.
'new peer's given ring' is the wordplay.
'new' indicates an anagram.
'given' is a charade indicator (letters next to each other).
'ring' becomes 'phone' ('phone' can be a synonym of 'ring'**).
'peers' with letters rearranged gives 'perse'.
'perse'+'phone'='PERSEPHONE'
'portraying' is the link.
(Other definitions for persephone that I've seen before include "having mobile that goes on by itself" , "Girl away all winter" , "Divine queen" , "#The wife from hell" , "wife of underground boss" .)