With which to clean up TV? (4)

I believe the answer is:

soap

I'm a little stuck... Click here to teach me more about this clue!

'clean up tv?' is the definition.
'soap' can be an answer for 'clean' (soaping is a kind of cleaning). I am not certain of the 'up tv?' bit.

I don't understand the rest of the clue.

Can you help me to learn more?

(Other definitions for soap that I've seen before include "Carbolic, perhaps" , "Popular TV programme (which cleans?)" , "TV programme; cleanser" , "Sudsy TV show?" , "made in a bar?" .)

I've seen this clue in the Evening Standard.

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