Dispatch a tiny drink astride horse (4)
I believe the answer is:
ship
'dispatch' is the definition.
(I know that dispatch is a more specific form of the action ship)
'a tiny drink astride horse' is the wordplay.
'a tiny drink' becomes 'sip' (I've seen this in another clue).
'astride' is an insertion indicator.
'horse' becomes 'H' (abbreviation as in horse power).
'sip' enclosing 'h' is 'SHIP'.
(Other definitions for ship that I've seen before include "Seagoing boat" , "Navigable vessel" , "See 18" , "Ocean vessel" , "craft of 1d [ADVENTURE]" .)