Running that may involve horse or mule or any across answer here? (4,9)

I believe the answer is:

drug smuggling

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'running that may involve horse or mule or any across answer here?' is the definition.
The definition suggests an adjective which matches the answer.

'running' is the wordplay.
I cannot quite understand how this works, but
'running' could be 'smuggling' (I've seen this before) and 'smuggling' is present in the answer.
The remaining letters 'drug' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...

Can you help me to learn more?

I've seen this clue in The Independent.

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