There are at least a couple of projects called Exist:

1) Exists is a Malaysian pop rock band formed in Johor Bahru, Johor in the end of March 1991. At that time, Exists was known as Exist (without letter 's' at the back) and the original members of this band is Mamat (vocalist), Along (guitarist), Shah (guitarist), Ajai (keyboardist), Musa (bassist) and Ujang (drummer). The band only changed its name to Exists when they release the 4th studio album titled Jangan Gentar in 1997.

2) 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).

3) A progressive death metal band from Baltimore, Maryland, USA. 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.
See Bandcamp for releases and more infos.

4) An indie band from the West Midlands, UK.
Band Members:
Matt : Lead Vocals, Guitar
Simon : Bass, BVs
James : Lead Guitar
Chris : Drums

5) A obscure Swedish metal band Read more on Last.fm. User-contributed text is available under the Creative Commons By-SA License; additional terms may apply.