Gall as old Greek character almost drowned in beer (3,5)
I believe the answer is:
oak apple
'gall' is the definition.
(I know that Oak apple is a gall)
I cannot understand how the rest of the clue works.
(Other definitions for oak apple that I've seen before include "Charles II's day?" , "Gall on tree containing wasp larvae" , "restoring the monarchy on this day!" , "growth made by wasp" , "Gall on some trees" .)