Not in the sense of other games. There is the arena and tag arena, where you can fight against other players - but you're not fighting against the human being behind them, they're AI-controlled.

If you're a new player, I'd recommend not spending too much effort on arena. You can build a basic cookie-cutter team with Khatun, Warmaiden, Spirithost, and your starter champ - that'll get you through the bot teams easily enough. But don't invest too heavily in leveling them. Focus on your dungeon/CB teams first.

if you are newer to the game, you want to set up for dungeons untill you get more well developed. When you hit mid game and have about 10 level 60's, then you can start the slow transition and endgame of course

Plus Plarium is messing with the Arena (Classic) matching system again. When I started I went to gold T4 with little problem and held it until Plarium broke the matching system about 9 months ago. It remained broken for over 3 months. After they fixed it finally, it only held about 4-5 months. They are messing with the rating system again and unless you have speed tuned teams with a 400 power rating and 6 star legendary gear you won't be able to get into Gold tier again. This is a very, very, very long discussion going on between players and Plarium. Plarium is looking at the $$, thinking that people will spend mass dollars to stay in gold tier which is pretty much the only way to upgrade your great hall. Over the last 1.5 years they have promised to give us other avenues to get great hall upgrades and better access to books which are critical in most cases but have never come through on any of their promises. So basically you're stuck with a Casino mobile game. If you don't spend thousands of $$ every month you can't compete.