Dizzy Delia entertains me, offering drink (7)
I believe the answer is:
limeade
'drink' is the definition.
(limeade is a kind of drink)
'dizzy delia entertains me' is the wordplay.
'dizzy' is an anagram indicator.
'entertains' means one lot of letters goes inside another.
'delia' anagrammed gives 'liade'.
'liade' placed around 'me' is 'LIMEADE'.
'offering' acts as a link.
(Other definitions for limeade that I've seen before include "Fruity drink" , "it's a soft one" , "Winter festival" , "Citrus drink" , "Non-alcoholic beverage" .)