Concorde will not fly again under any circumstances, as Airbus (the engineering and design authority for the aircraft) will not support it. That completely overrides any individual or corporate ambition for the aircraft.
There will not be a supersonic replacement for Concorde until the problems of supersonic flight over land ('sonic boom'), excessive fuel consumption and environmental effects are addressed and solved. Research into these areas is ongoing and has a direct impact on military aircraft design, so the techniques will be developed. Once they are, the aerospace industry will start prompting the airlines to consider a new supersonic aircraft. I would guess that you'll have to wait 50 years or more to next see one in commercial service - and the concept may by then have been overtaken by extra-atmospheric flight.