Normally Steam-based servers should update themselves. However, if you have to restart an update, or if you do not want to wait for the auto mechanisms, then you can trigger the process manually with the Submenu item "Update Master App".
To do this, first select the app or game masters to which you want to update. The selection automatically adjusts the list of "Master Apps".
In the second step then the game or games to be updated. After the selection is complete, click on the button "Refresh"