Can I point a newly bought domain name to a sub domain?

[sandpetra]

Can I point a newly bought domain name to a sub domain of a site I already own and operate?

[Mistra]

I don't see your question is relevant to Google Adsense but to answer your question, yes you can. Some registrars have URL forwarding services that you can forward your newly bought domain to any domain you want including your other sub domain.

Go to your registrar control panel and look for URL forwarding. If your hosting plan allows "unlimited domains" to be hosted then you can point it to your other subdomain too. In this case you just need to change your nameservers at your registrar to point to your web host and do the necessary pointing to your sub domain from there.