Can I use music clips by other artists without their permission?

Dear Questioner, Generally NO, you need to license anything you want to use. But if you think what you're using may be covered under FAIR USE, you should really sit down and discuss it with an attorney. There are very few 100% clear examples of fair use, and it doesn't sound like you have one, so you'll need to consult. Licensing clips is often inexpensive and worth looking into.

No, you cannot use music clips in a TV show without permission. This permission is called a Synch License, or Synchronization license. You must get a Synch license from two entities: 1) from the owners of the copyright on the song. This can be the publisher or the songwriter, if there is no publisher. Sometimes a song can have multiple copyright owners. 2) from the copyright owner of the Sound Recording. This is often the record label. If there is no record label, it might be the artist. You should have a lawyer help you with these synch licenses. You can also hire a clearance company to get the for you. You should also purchase E&O insurance (errors and omissions) to cover any mistakes in the clearances. A copyright owner can refuse to give you a synch license and they can charge any price. If you do get synch licenses, you should also fill out cue sheets so the songwriters are paid their proper royalties. You should get a music lawyer to help you with all of this. It is very complicated. If you do it wrong, your show becomes worthless and cannot be shown or marketed.

You cannot. It's copyright infringement.