Yes, there are premium only arenas. You can find them in the tournaments just like the other arenas or go to play > tournament > schedule to see the ones you are interested in joining and the time it will be starting.
Are there premium only arenas?
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I cannot find even a single one. They are all open to everyone and not only premium members.
Jun 11, 2023
0
#4
Arenas with the Diamond symbol are premium only arenas. As at when you made this thread there was a 3/2 blitz premium only arena about to start, it has ended now. 
Then there’s a bug with my account because I don’t see those.
Jun 11, 2023
0
#6
I don't think your account is bugged. If you are using the website, go to https://www.chess.com/play/online Click tournament and you will see list of current tournaments. You will also see the 5|5 premium only tournament. It has started now. On phone, click play, tournament and you will see the 5|5 tournament.
Oh I see the problem. In the app there’s no diamond. Only on the website it’s visible. 
AghaPerham wrote:
I feel so inadequate playing in normal arenas where most 1200 players joined yesterday play like grand masters with very quick reactions. Is it possible to play in premium only arenas where I can play with people my own level without god-mode on?
Disconnecting coward. I love how you're so entitled that you think you can come here and provide actual insight when on the board when you are playing with your opponent's you're an absolute toxic PoS that abandons games when you are lost. Garbage person.
I feel so inadequate playing in normal arenas where most 1200 players joined yesterday play like grand masters with very quick reactions. Is it possible to play in premium only arenas where I can play with people my own level without god-mode on?