One's strange daughter was inquisitive (5)
I believe the answer is:
nosed
'was inquisitive' is the definition.
(I've seen this in another clue)
'one's strange daughter' is the wordplay.
'strange' is an anagram indicator.
'daughter' becomes 'd' (genealogical abbreviation).
'ones' is an anagram of 'nose'.
'nose'+'d'='NOSED'
(Other definitions for nosed that I've seen before include "Checked wine's aroma" , "Snooped" , "Beginner" , "See 1 Across" , "Scented" .)