I can able to see that xldeploy module in puppet supports
installation/service/configuration files for XL Deploy
xldeploy repository configuration items
xldeploy repository roles/permissions
xldeploy repository dictionaries
xldeploy cli installation
installs compatible java version (optional)
Link: https://github.com/xebialabs-community/puppet-xldeploy
How can i do a application deployment using puppet through deployit? or any other way to do it through automation?
As you've discovered, the XL Deploy puppet plugin is meant to manage an XLD server installation. It is not a plugin that enabled deployments via puppet. The standard XL Deploy plugins do not provide this capability.
If you did want to trigger a puppet command to perform a deployment from within an XL Deploy deployment plan, I suggest you look into using rules (see https://docs.xebialabs.com/xl-deploy/concept/getting-started-with-xl-deploy-rules.html).