There are at least a couple of projects called Exist:

1) In 2001, noCore teamed up with D-Trash artist Schizoid to form Exist, which released 2 albums, "Exist" (2001) and "The Tension and the Darkness" (2001).

2) A progressive death metal band from Fredrickburg, Maryland, the United States of America. Their music is available free at their website and is streamed at their Bandcamp. The members of the band are Max Phelps on guitars and vocals, Alex Weber on bass and vocals, Matt Clise on drums and Matt Rossa on guitars.

3) An indie band from the West Midlands, UK.

Band Members:
Matt : Lead Vocals, Guitar
Simon : Bass, BVs
James : Lead Guitar
Chris : Drums

Influences:
Primal Scream, Death In Vegas, Kasabian, The Music, Stone Roses, Doves, Chemical Brothers

Sounds Like:
exist "Best New Band In Britain" - Steve Lamacq Radio 1 "Woooosh what the f*ck was that" The Fly "Absolutely astounding band to fall in love with"

Visit their site:

www.exist.tv

4) A obscure Swedish metal band