The correct and best way for your client to proceed, if the client has any desire for this image to be identified with his business and only his business, would be to either locate the creator of the image and see if exclusive rights can be acquired or to hire an artist to create something similar but original and then sell your client all rights to it.
Snagging images off the internet is almost always a copyright infringement. Using clipart under license is a step up but does not include any rights to claim ownership of the intellectual property.
Having covered that, converting any image to a vector is not a need that lends itself to a single one size fits all solution. It depends on the nature of the art and the desired look of the vector. If you are in need of developing the skills to do this, there are lots of tutorials showing as many different approaches. If you need the work done and don't have time to learn to do it first, hiring the
Vector Doctor is your shortest path to an immediate solution.
