In short, beginning to reduce horse's pace (4)
I believe the answer is:
trot
'horse's pace' is the definition.
(I've seen this before)
'in short beginning to reduce' is the wordplay.
'in' means one lot of letters goes inside another.
'short' becomes 'tot' (both can mean a small alcoholic drink).
'beginning to' says to take the initial letters.
The first letter of 'reduce' is 'r'.
'tot' placed around 'r' is 'TROT'.
(Other definitions for trot that I've seen before include "Clip (horse)" , "Slowish run, of horse or person" , "Communist - horse pace faster that a walk" , "moderate movement" , "(Horse's) moderate pace" .)