Thanks for reaching out to the Community, RachelFP.
 

Since your account's integrated with QuickBooks Online Payroll, you'll need to make the employee inactive in your payroll subscription to archive them in QuickBooks Time.
 

Here's how:

1. In the left navigation bar, go to Payroll or Workers, then access your Employees screen.
2. Find and click the employee's name.
3. Next to Employment, hit Edit (✏️). If you don't see your Employment tab, check if you have paychecks created. You'll need at least one paycheck to change employment information.
4. Use the Status drop-down list, then choose an appropriate status.
5. Select Done.

I can certainly understand how an ability to archive team members inside of QuickBooks Time with QuickBooks Online Payroll integration could be useful and have submitted a suggestion about it as of today.
 

You can also submit your own feature requests while signed in.
 

Here's how:

1. In the left navigation bar, go to My Team or Customers.
2. Click your Suggest Idea button.
   
3. Enter the suggestion(s) in your Idea field.
4. Select Send Idea.
   

Your feedback's definitely valuable to Intuit. It will be reviewed by our Product Development team and considered in future updates. You can stay up-to-date with the latest news about your products by reviewing Intuit's Product Updates webpage.
 

Please don't hesitate to send a reply if there's any questions. Have an awesome day!