One’s odd daughter snooped (5)
I believe the answer is:
nosed
'snooped' is the definition.
(I've seen this in another clue)
'one's odd daughter' is the wordplay.
'odd' 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 "Moved slowly and cautiously forward" , "Move back or away" , "Eased" , "Nodes (anag.)" , "proceeded cautiously" .)