Though using a gold border is nice (and I don't think you should remove it) it may not be very obvious to people. I assume that you want it to be quite noticeable in order to get more people to upgrade to a premium account.
Is there anywhere that you show more info about the user?
For instance on ux.stackechange the users name, rep, badges are shown next to the avatar and (for those users with higher rep) rollover shows even more info.
If you already show more info then this would be the place to add it either as a badge with a tool tip or just as text saying 'Premium Member'.
If you do not show more info then I would suggest one of several options:
- Add more info about the user either next to their avatar or on rollover as mentioned above.
- Add a small badge (icon) somewhere on or near their avatar (though be careful - on the avatar can interfere with it). This would be just like the badges that you see here on ux.stackexchange. Be sure to include a tool tip as an icon on its own is not always clear as to its meaning.
- Add the text 'premium member' just below or next to their avatar.
If you do want more people to upgrade then it would be worth linking any mention of premium members to more information about what the benefits are and an opportunity to sign up.