When EntraPass needs an update it will show a screen similar to the below image. This should not require admin permission, so any user should be able to update it. To install the update, click on the "Download" button as show in the image below.

Clicking "Download" should bring you to the below site: 

Once you start the download, click "Run", accept the terms and conditions and click "Next," "Just me" installation is fine to choose. Click "Next" one more time and the installation will begin. This may take a few minutes, and you will have to click "Next" once again after it has completed.