To update Timesheets, you need Jira System Administrators permissions:
Log in as a user with the Jira Administrators global permission.
Click on the
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gear icon at top-right and select Add-ons.
On the left sidebar, click on Manage add-ons.
Under User-installed add-ons, select Tempo Timesheets.
Click on Update. If there is no update option listed under Tempo Timesheets then your version of Timesheets is up to date.