Did not relish being kept without date? Not half (5)
I believe the answer is:
hated
'did not relish' is the definition.
(hating is the opposite of enjoying or relishing)
'kept without date? not half' is the wordplay.
'kept' becomes 'had' (I've seen this before).
'without' means one lot of letters goes inside another ('without' can be similar in meaning to 'outside').
'not half' means to take half the letters.
'date' cut in half is 'te'.
'had' going around 'te' is 'HATED'.
'being' acts as a link.
(Other definitions for hated that I've seen before include "Seriously disliked" , "Death (anag)" , "was unable to stand" , "Abhorred" , "Loathed" .)