If I set up a custom domain, does it replace my existing website?

No. A custom domain is used for your portal and your client-facing pages, such as your sign-up link and client emails, so your existing website stays exactly where it is and keeps working normally. You set it up in your portal settings, where the platform generates the DNS records for you to add at your domain provider. Those records only apply to the domain or subdomain you enter, so they do not touch the records serving your main site. For the steps, see "How do I connect a custom domain so my client portal uses my own web address?".