Horse initially brought to Troy under volatile monarch (5,5)
I believe the answer is:
henry tudor
'monarch' is the definition.
(Henry VII or Henry VIII)
'horse initially brought to troy under volatile' is the wordplay.
'initially' suggests taking the first letters.
'brought to' says to put letters next to each other.
'volatile' indicates anagramming the letters.
The first letter of 'horse' is 'h'.
'troy'+'under'='troyunder'
'troyunder' anagrammed gives 'enrytudor'.
'h'+'enrytudor'='HENRY TUDOR'
(Other definitions for henry tudor that I've seen before include "Old sovereign" , "King" .)