Having started my consulting journey a few months ago and received paid clients, there several ways to drive traffic to your profile (and to answer your question, when you start out, yes you have to drive your own traffic to your profile).
The first place to share this website is through your LinkedIn profile if you are comfortable doing so. LinkedIn is the leading business platform that allows you to network with many professionals and potentially drive traffic to your clarity profile.
If you have a professional website, I would also link your clarity.fm profile to that website.
You also have to ask yourself, why would somebody want to visit my profile? What skills do I bring to the table that is of value to people? After answering those questions, you have to think about how to market to your target audience and grab their interests.
At the beginning of your consulting journey, you need to be a "hunter" and aggressively network/seek out the right folks to build out your personal brand. After establishing your credibility, then people will start coming to your site.
Happy to jump on a call and help you strategize.
It sounds like you're listed on Clarity?
If that's the case, yes, you must do your own marketing to attract potential connections.
If you're trying to generate interest outside of this platform, I would point people to your Clarity Answers page. That will reflect your expertise fairly well.
Good luck and please let me know if you need more assistance – I’ve trimmed my rate in response to the current global uncertainties.