Dismay of single daughter in private (10)
I believe the answer is:
intimidate
'dismay' is the definition.
(thesaurus)
'single daughter in private' is the wordplay.
'single' becomes 'I' (one).
'daughter' becomes 'd' (genealogical abbreviation).
'in' means one lot of letters goes inside another.
'private' becomes 'intimate' (similar in meaning).
'i'+'d'='id'
'id' inserted within 'intimate' is 'INTIMIDATE'.
'of' is the link.
(Other definitions for intimidate that I've seen before include "Frighten" , "Threaten" , "Strike fear into" , "Scare" , "Bully" .)