premier (adjective): first, especially for rank, time and importance
They supply only the premier business resources.

premier (noun): a political leader of prominence
Each Australian state has a Premier.

premiere (noun): the first public performance, usually relating to a play, music or movie
He was very excited to be invited to the premiere last week.

While premiere is very specific, the word premier can be used a number of ways – the adjective premier could even be use to describe the first performance although accepted usage indicates premiere as the preferred option.