For example, a daughter giving antiquated oath (4)
I believe the answer is:
egad
'antiquated oath' is the definition.
(I've seen this in another clue)
'for example a daughter' is the wordplay.
'for example' becomes 'eg' (short for 'exempli gratia', 'for example' in Latin).
'daughter' becomes 'd' (genealogical abbreviation).
'eg'+'a'+'d'='EGAD'
'giving' acts as a link.
(Other definitions for egad that I've seen before include "Archaic exclamation of surprise" , "Old exclamation; aged (anagram)" , "My word once" , "Oath sworn" , "Mild oath - aged (anag)" .)