The easiest way to find your first client for a psychologist is to register on a large psychological forum. On such forums, thousands of people are looking for psychological help every day. At least 10% of them are ready to pay for the work, including beginning psychologists.
I'm not a psychologist, but I periodically read blogs / websites of various specialists. As an option, I noticed that now many psychologists set up their own accounts on Instagram, where they post short articles and conduct broadcasts. You can also host free webinars where you can offer your services. There is also the B17 website, where you can consult a client for free and invite him to a normal consultation.
Any private consulting services can be perfectly promoted through thematic communities - forums, groups, etc. It is important to spare no effort at the start. If you offer services for free for a certain period, you can get honest recommendations from free customers in the community and after a while start adding to free paid ones. Well, and gradually completely replace the second with the first. I had a similar successful experience with private lessons.