Horse carrying short playwright (7)
I believe the answer is:
marlowe
'playwright' is the definition.
(Christopher Marlowe, 1564-1593)
'horse carrying short' is the wordplay.
'horse' becomes 'mare' (mare is a kind of horse).
'carrying' indicates putting letters inside.
'short' becomes 'low' (associated in meaning).
'mare' going around 'low' is 'MARLOWE'.
(Other definitions for marlowe that I've seen before include "writer" , "Christopher --, English playwright" , "Christopher -, playwright (Tamburlaine)" , "English poet" , "Kit" .)