We need to deploy our application on Tomcat. How can we package the application as WAR?

Although this is not supported by default in Play, we can use the play2-war-plugin module (refer to https://github.com/play2war/play2-war-plugin/) to achieve this.

Is there a simpler way to deploy the application on PaaS?

Deploying Play applications on Heroku, Clever Cloud, Cloud Foundry and/or AppFog are documented at https://www.playframework.com/documentation/2.3.x/DeployingCloud.