In a newgame+, what happens to promoted MP characters?
Your promoted characters are shared across all your single player games in the form of war assets. Once you reach the point that you can use your war room, you'll be able to see them listed under N7.
This will also mean that its entirely possible to completely lock yourself out of seeing any ending other than the 'best' ending due to having too many war assets from promotion (but it would take a LOT).