world
American, British, etc.
film (esp. BrE), movie (esp. AmE), television, TV
stage, theatrical (esp. AmE)
the stage premiere of John Adams's opera
the movie's theatrical premiere (AmE)

season (esp. AmE)
Did you catch the season premiere of ‘The Sopranos’?

gala
the gala world premiere of the movie

glittering, glitzy, star-studded (all esp. BrE)
London hosted the star-studded premiere of ‘Harry Potter’.

attend
They attended the premiere together.

host, present
conduct
He conducted the world premiere of the symphony.

give (sth its)
The opera was given its premiere by the New York City Opera.

receive
The movie receives its American premiere on November 16.

episode, issue (both esp. AmE)
the premiere episode of ‘Angel’
the premiere issue of a new journal

party
the movie's premiere party

Premiere is used with these nouns as the subject:
film