Your question is tagged to Intuit Online Payroll, but you mentioned about updating payroll, so I'll take this as QuickBooks Desktop Payroll. Did you get any prompt when you tried downloading the update?
You can try re-validating your payroll service key to refresh your payroll. This step will also download the payroll update.
Press Ctrl + K while QuickBooks is open.
On the QuickBooks Service Keys window, select the Edit button.
Click Next and remove the check mark in the Open Payroll Setup box on the next page.
Click OK in the previous window.
If it's the same thing, you can visit the Account Maintenance page to see the status of your payroll service and billing details.
From the Employees menu, choose My Payroll Service.
Select Account/Billing Information.
Log in using your Intuit credentials.
Check the status of your payroll, and then billing details.
If everything looks good, please log out to refresh your payroll service and re-sync your billing details. If the issue persists, please contact our Phone support or Chat team to check this further.
You can always go back to this thread if you have other questions.