Yes, you can close your Client account and create a new Client account on your existing Freelancer account. You can be a Client and a Freelancer using the same account. You'll use the same account to log in to Upwork, but the two parts of your account will be kept entirely separate. You'll be able to easily switch between the two as needed. To create a Client account on your existing account, please follow up instructions in this help article.
A change of terminology might be in order. It's confusing to talk about a "client account" and a "freelancer account" both being the same account, or parts of the same account. Perhaps they could be called the "client role" and the "freelancer role" of one account.
I understand where you're coming from with this suggestion. However, based on my experience, "account" and "profile" are the most commonly used terms when referring to the freelancer/client/agency contexts. Our users are coming from different backgrounds, in which different terms are used to describe the same phenomenon and same terms are used to refer to different ones, we exercise additional caution and try to clarify as clearly as possible what a user is referring to and what we're describing in our responses.
I can see how "role" can be less confusing for some users since account is referring to the user's Upwork account in general, but also how, due to the sparse use of the term in this context on Upwork and elsewhere (judging from my personal experience) can create confusion for other users. We do appreciate your feedback and look forward to a productive exchange of ideas on this subject, which we'll take into consideration and also share with our product team.