I created a new instance and restored the backup from old instance of Discourse to the new one (Discourse version is same and has the same set of plugins).
But all users profile pictures went empty. Users who had attached their pic with gravatar, have their setting changed to ‘Custom Picture’ (which is empty). And users who had a customized picture, too have lost that profile picture.
Edit: On the new site, I’ve not yet implemented the Google/FB sign in buttons yet, in case that has anything to do with gravatar profile pics.