conscious: (adjective aware of a situation or of one’s surroundings; awake; alert
conscience: (noun) inner thoughts or feelings that lead you to speak or act in a way that is in keeping with your beliefs; an inner sense of right and wrong
The noun form of the adjective conscious is consciousness. That is what you would regain if you had been asleep, knocked out, or in a coma. Hopefully you will never lose your conscience, and therefore you won’t need to regain it.