There's no button to make a new API key for an existing project. A project's API key never changes, even when you change its auth method or IP Whitelist, or transfer it to another workspace. To replace a key, you move to a new project and remove the old one.
Replace a key
Go to New Project, choose the same Auth Method and IP Whitelist as the old project, and click Create Project. Make sure you're in the same workspace (Personal or the team), so runs keep charging the same wallet.
Copy the new API Key and API Secret and put them in your app, server or tool.
Run a request with the new key and check that it works.
On the Projects page, open the old project's menu, choose Remove and confirm with Remove.
The old key stops working as soon as the project is removed. Removing can't be undone, so switch everything over first.
What stays the same
Tasks and results belong to your account or team, not to the project. Tasks you ran with the old key stay in Task History, and the new key can read them.
Your balance is in your personal wallet or the team wallet, not in the project, so nothing needs to be moved. The old project disappears from the project filters and from the per-project list in Project Usage, but its past charges still count in your totals.
Good to know
Lost your secret, but it hasn't leaked? You don't need a new project. On the Projects page, click the eye icon next to API Secret and confirm it's you with your password or a 4-digit code we e-mail you.
Changing the IP Whitelist gives the project a new API Secret and the old secret stops working at once, but the API Key stays the same. On an API Key Only project the key alone authorizes requests, so this doesn't help if the key leaked.
Team projects: any member can create a project, but only team admins and the organization owner can remove one or see its API Secret again.
More: How do I get an API key?