If you apply for something, but the organization you're applying to says "no", then they've "denied" your application:

My financial aid application was denied.

This phrase can be used when talking about applying for things from the government like financial assistance, licenses, permits, etc.

However, applying for a job is different. If you apply for a job but don't get it, the company hasn't "denied" your application.

The noun form of "deny" is "denial", so you can also talk about "denial of an application":

Denial of an application is final. You may not re-apply.