Reduced pace of horse on course (5)

I believe the answer is:

troon

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'course' is the definition.
(Royal Troon Golf Club, a golf course)

'reduced pace of horse on' is the wordplay.
'reduced' means to remove the last letter.
'pace' becomes 'trot' (I've seen this before).
'of' becomes 'o''.
'horse on' becomes 'n' (I can't explain this - if you can you should believe this answer much more).
'trot' with its final letter taken away is 'tro'.
'tro'+'o'+'n'='TROON'

Can you help me to learn more?

(Other definitions for troon that I've seen before include "Coastal town of West Scotland" , "Scottish golf town" , "Ayrshire golf course" , "West Scottish town with links" , "Open home" .)

I've seen this clue in The Times.

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