Both the Chrome app, and the native OSX, Windows, and Linux apps can be force-upgraded. To find the current version of your app, head to Settings (top-right corner of the app) > About.
Chrome apps generally update automatically. To force an update, check https://www.getpostman.com/docs/postman/launching_postman/installation_and_updates#chrome.
Native apps (OSX, Windows, Linux) will show you a popup when an update is available. This can also be accessed through the Settings > Update tab. Documentation for this is at https://www.getpostman.com/docs/postman/launching_postman/installation_and_updates#native-app-mac-windows-and-linux.