Consumed drop of daiquiri after daughter went out (5)
I believe the answer is:
dated
'went out' is the definition.
(dating is a kind of going out)
'consumed drop of daiquiri after daughter' is the wordplay.
'consumed' becomes 'ate' (eating is a kind of consuming).
'drop of' says to take the initial letters.
'after' means one lot of letters go next to another.
'daughter' becomes 'd'.
The first letter of 'daiquiri' is 'd'.
'ate'+'d'='ated'
'ated' after 'd' is 'DATED'.
(Other definitions for dated that I've seen before include "Old-fashioned" , "Passe" , "No longer fashionable or current" , "Antiquated" , "Unfashionably old" .)