Mesmerising person trained this pony over time (9)
I believe the answer is:
hypnotist
'mesmerising person' is the definition.
(I've seen this before)
'trained this pony over time' is the wordplay.
'trained' is an anagram indicator (train can mean to shape or manipulate).
'over' is an insertion indicator.
'time' becomes 't' (abbreviation).
'this'+'pony'='thispony'
'thispony' with letters rearranged gives 'hypnoist'.
'hypnoist' enclosing 't' is 'HYPNOTIST'.
(Other definitions for hypnotist that I've seen before include "stage entertainer" , "One who mesmerises" , "Mesmerising person" , "Mesmeriser" , "charmer" .)