Author getting to grips with end of script before a drink (5,3)
I believe the answer is:
green tea
'drink' is the definition.
(type of tea)
'author getting to grips with end of script before a' is the wordplay.
'author' becomes 'greene' (Graham Greene, 1904-1991).
'getting to grips with' means one lot of letters goes inside another (one group of letters grips another).
'end of' says to take the final letters.
'before' means one lot of letters go next to another.
The last letter of 'script' is 't'.
'greene' enclosing 't' is 'greente'.
'greente'+'a'='GREEN TEA'
(Other definitions for green tea that I've seen before include "Infusion" , "Infused drink" , "Brewed" , "Drink - generate (anag)" , "Teen rage (anag.)" .)