I have been using the Desktop App and recently the application shows the message upon starting up
“This Chrome App is being deprecated”.
What does this mean?
Will the desktop app be pulled down/not supported in future?
Can I continue to use it ? I do not want to download the native app.
Ah, just re-read what you posted.
The Chrome app, will be deprecated. You should definitely move to the Native app, as the Chrome app won’t be receiving the latest features/bug fixes etc.
Ok, but at least whatever the chrome app supports, it will continue to support?
I am not looking for the chrome App to get additional bug fixes or latest features, but at least can I continue to use it as is?
I think this should answer your question 
https://support.getpostman.com/hc/en-us/articles/115005873349-What-does-the-Chrome-app-deprecation-mean-for-me-