Imagine, my dear, a rum after end of round (8)
I believe the answer is:
daydream
'imagine' is the definition.
(daydreaming is a kind of imagining)
'my dear a rum after end of round' is the wordplay.
'rum' is an anagram indicator (rum can mean strange or unusual).
'after' is a charade indicator (letters next to each other).
'end of' suggests the final letters.
The final letter of 'round' is 'd'.
'my'+'dear'+'a'='mydeara'
'mydeara' anagrammed gives 'aydream'.
'aydream' after 'd' is 'DAYDREAM'.
(Other definitions for daydream that I've seen before include "Diurnal reverie" , "A pleasant diurnal fantasy" , "(Indulge in) idle reverie" , "Diurnal reveries" , "An idle diurnal fantasy" .)