Gore beginning to drop into tube (5)
I believe the answer is:
vidal
'gore' is the definition.
(writer Gore Vidal, 1925-2012)
'beginning to drop into tube' is the wordplay.
'beginning to' says to take the initial letters.
'into' indicates putting letters inside.
'tube' becomes 'vial' (tubular or cylindrical container).
The initial letter of 'drop' is 'd'.
'd' put into 'vial' is 'VIDAL'.
(Other definitions for vidal that I've seen before include "Gore, US writer" , "Gore - - , uthor" .)