To perform in order to display one's abilities in an attempt to be granted a role in something (typically a role in a play). Are you auditioning for this year's spring musical? I'm going to sing that song when I audition for the play.
audition someone for something
to allow someone to try out for a part in a performance; to judge someone's singing, speaking, or playing potential for a part in a performance. Will you audition anyone else for the part? Have you been auditioned for a part in the school play?
audition for something
to try out for a part in something. (In a setting in which one's singing, speaking, or playing is heard and judged.) I plan to audition for the lead role in the school play. Liz auditioned for The Mikado.