When a public office-holder leaves office, they are subject to certain rules administered by Commissioner Dion. I would say the only thing they are prohibited from doing is lobbying, given that a lobbyist is in contact with public office-holders.
Of course, an MP will have built relationships with their fellow members and acquired an understanding of internal workings. The purpose of the rule is to prevent the hiring organization from deriving an unfair advantage because the individual held public office. That would disadvantage other people who could also be doing the work. You can work for organizations, but you cannot become a lobbyist.