When you purchase an application from the PlayStore, it is registered in your PlayStore account. This means you can always reinstall it on your device, or install it on a new device, without having to buy it again.
To reinstall the application, open the PlayStore and go to your account:
Once in your account, go to Manage apps and device :
Go to Manage and select Installed to give you the option of selecting uninstalled applications:
Select the application you wish to reinstall, then select the download icon:
