Well there are many servers you can deploy your grails application.
Here i will use Jelastic to demonstrate deploying grails application
1 Got to jelastic.com Sign up for an account
2 After successfully creating an account log in to your account i have used jelastic’s layershift service
3 now first you need to create environment for deploying your application
4 now select Tomcat and database you are going to use
5 now you have created environment upload war file to deploy