If an update for Edge is available, Edge will need to be closed in order for the process to complete. To do so, either click the Windows logo in the bottom-left corner of the screen or press the ⊞ Win key. It's in the lower-left corner of the Start window. Doing so will open the Settings page. You'll see this option near the bottom of the Settings page. It's a button near the top of the Update & Security page. Once you see "Your device is up to date" displayed at the top of the page, your Microsoft Edge browser has been updated.

Summary:
Close Microsoft Edge if it's open. Open Start. Click ⚙️. Click Update & security. Click Check for updates. Wait for the updates to finish installing.