Aristo on horse having tot (5,2)

I believe the answer is:

count up

'tot' is the definition.
(to tot is to add or count up numbers)

'aristo on horse' is the wordplay.
'aristo' becomes 'count' (a count is a type of aristocrat).
'on horse' becomes 'up' (up can mean mounted on a horse).
'count'+'up'='COUNT UP'

'having' is the link.

I've seen this clue in The Independent.

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