Not half elated on daughter getting engaged (5)
I believe the answer is:
hired
'engaged' is the definition.
('hire' can be a synonym of 'engage')
'not half elated on daughter' is the wordplay.
'not half' means to take half the letters.
'elated' becomes 'high' (similar in meaning).
'on' becomes 're' (regarding).
'daughter' becomes 'd' (genealogical abbreviation).
'high' with half the letters taken is 'hi'.
'hi'+'re'+'d'='HIRED'
'getting' is the link.
(Other definitions for hired that I've seen before include "Chartered" , "Engaged for wages" , "Employed for wages" , "Taken into service" , "Paid to work" .)