If you're aspiring, you're trying to be something. If you're an aspiring singer, you're probably out booking as many gigs as possible in the hopes that someone will soon discover you.
The adjective aspiring describes a person who wants to succeed at a particular goal, often one related to a career. Many aspiring artists move to New York City in the hopes that they'll get into a major gallery and sell their art. Aspiring country musicians move to Nashville to try to land a recording deal. If you're an aspiring politician, you may study political science and intern at the state senator's offices to gain experience and make connections.