What does your license cover? A CD has two copyrights associated with it -- one for the "musical work" and one for the "sound recording." The copyright on the musical work -- that is, the song, is usually owned by whoever wrote the song -- so if the band wrote the song, the band owns the copyright, unless they sold it or otherwise exclusively licensed it to someone else.
The actual recording of the song for the CD has a seperate copyright associated with it, and that copyright is usually owned by whoever paid to have the CD recorded -- usually a record label. In this case, you would have to have a license from the record company to put a clip of the song on your website (I'm assuming, of course, that you own the copyright for the musical work and would be willing to grant yourself license to use it!).