Turn image into vector without losing quality?

My client got a drawing he uses as a logo, it’s present on some of his socials posts and he also uses it as a profile picture.
I’m currently working on updating their flyers and i’d like to add the logo on it cause it wasn’t present before.
My problem is they told me on the phone they do not have the source document for the logo with the outlines and so on and seemingly been using a copy pasted jpg/png on all their posts (I think they used to make them themselves, it’s a small business).

I would just know what the best technique would be for me to turn it into a trace (using a png/jpg) that me or them could reuse in future productions without losing the quality and colors?

Thanks in advance!

There is no quick fix. Usually you will have to redraw it, is it something you can share? If so then people can better advise the best way to recreate it.

It shouldn’t be too much of a problem since it’s all over their pages but i’ll just share half of the drawing just in case

Looks to me like a pipe puffing out black and white smoke.

Your client is a tobacconist?

Well, the good news is it appears to be all vector and flat color. For an actual logo it does seem pretty complex, but with some time and effort, you could probably recreate that in Illustrator.

I don’t suppose they have an existing PDF floating around with the logo that may have an early vector based version embedded. If so you can open the PDF in Illustrator and copy it into a separate standalone logo file.

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Since it is half the logo, it looks (to me) like a woman sitting in profile wearing blue pants and a patterned shirt.

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ahah I could see it but no it’s a woman sitting, he owns a bookstore

Well, there lies the problem, but since this has nothing to do with your request, @CraigB has the right solution.

Oh, I love what Google spits out in image search to that. #Slightlyofftopic