I can only speak from the perspective of someone running a music marketing agency, hopefully, it will be helpful. Occasionally we hear from artists who want their music video to be promoted. We have to pass on such requests, as from our point of view promoting a single piece of content doesn't make sense. To be clear, there are companies who will be able to promote your music video, as long as you have a clear understanding of what exactly you mean by video promotion. For example, there are companies who will help you optimize a video for search, or who will drive views on the video through ads or video seeding (beware of fake views, it's still quite common and besides harming your Channel by bringing bot views you risk the video being taken down by YouTube).
If you want more sustainable results, consider running a bigger campaign, which will have to include more than one music video release; you could mix it up with single, EP or LP releases, or a tour. For that, find a digital marketing agency or a PR agency, preferably both. A marketing agency will help you better craft your brand and grow your online following and turn more of your followers into genuine fans. A publicist will help you appear on various media resources; a proper music video will surely make that work easier.
With most agencies, you pay a monthly retainer. It's quite difficult to generalize the prices. The fee depends on the company and the scope of the campaign. Always get a quote from anyone you consider working with to get an idea. Usually, it won't be difficult and won't require a lot of time to get at least a range, without committing to anything. So think of why you really want to hire a promotional agency of any sort for and shop around!