Dignitary has to praise horse in speech (4,5)
I believe the answer is:
lord mayor
'dignitary' is the definition.
(I've seen this before)
'to praise horse in speech' is the wordplay.
'to praise' becomes 'lord' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'horse' becomes 'mare' (mare is a kind of horse).
'in speech' shows a homophone (sound like).
'mare' is a homophone of 'mayor'.
'lord'+'mayor'='LORD MAYOR'
'has' acts as a link.
Can you help me to learn more?
(Other definitions for lord mayor that I've seen before include "Municipal official" , "head for city" , "Showman" , "magistrate" , "Title of first citizen of a city" .)