Caught horizontal with US president, once (9)

I believe the answer is:

cleveland

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'president once' is the definition.
(I know that Cleveland is a Chief Executive)

'caught horizontal with' is the wordplay.
'caught' becomes 'c' (cricket abbreviation).
'horizontal' becomes 'level' (similar in meaning).
'with' becomes 'and'.
'c'+'level'+'and'='CLEVELAND'

'us' acts as a link.
This may not be right. It may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for cleveland that I've seen before include "past president" , "US city" , "Northeast English county, created 1974" , "former President" , "Large city of Ohio" .)

I've seen this clue in The Telegraph.

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