Yes, it’s illegal
Public performance is one of the rights covered by copyright.
A piano arrangement is a derivative work and receives its own copyright protection independent of the original work. So, if I were to write an arrangement of Beethoven’s Fur Elise (which is public domain), my arrangement would be protected by copyright - specifically the choices I made that are not in the original work - you would need my permission to play it in public. If I were to write (with permission) an arrangement of Billy Joel’s Piano Man (which is under copyright) you would need the permission of both of us to play that arrangement.
Most jurisdictions have a mechanical copyright system for paying royalties to composers. That is, you can get a licence (permission) to play any music by contacting the administrator of that scheme and paying the appropriate royalties.