Twice actor oddly rejected a drink (5)
I believe the answer is:
cocoa
'drink' is the definition.
(cocoa is a kind of drink)
'twice actor oddly rejected a' is the wordplay.
'twice' indicates the doubling of some letters.
'oddly rejected' means one should take alternating letters (letters in odd-numbered positions removed).
The alternating letters of 'actor' are 'co'.
'co' doubled is 'coco'.
'coco'+'a'='COCOA'
(Other definitions for cocoa that I've seen before include "Popular chocolate drink" , "Hot bedtime drink" , "It's made from the seed of the cacao tree" , "Medium to dark brown" , "Chocolatey drink" .)