One divining secrets unfamiliar to her daughter (7-6)
I believe the answer is:
thought-reader
'one divining secrets' is the definition.
The answer is a person as well as being a singular noun. This is suggested by the definition.
'unfamiliar to her daughter' is the wordplay.
'unfamiliar' is an anagram indicator.
'to'+'her'+'daughter'='toherdaughter'
'toherdaughter' anagrammed gives 'THOUGHT-READER'.
Can you help me to learn more?
(Other definitions for thought-reader that I've seen before include "One discerning another's mind" , "A looker into minds" , "One who knows what we have in mind" , "Telepath" , "One looking into others' minds" .)