But I would start by choosing how and whether to fix up the crown jewels, the database.
You say that instead of adding columns, team has been adding new tables instead. With such behaviours, it's possible your database is such a steaming pile of crap that you'll be unable to move at any pace at all until you fix the database. Certainly if management want e.g. reporting tools added, you'd be much better to fix the database first. On the other hand, if the new functionality doesn't require significant database interaction (maybe you're just tarting up the front end and adding some eye candy) then maybe you can leave it be. Unlikely I would imagine.
Do not however just leave the database as a steaming pile of crap, and at the same time start writing a whole lot of new code against it. Every shitty database design decision made over the previous years will echo down and make it's ugly way into your new nice code. You will be better for the long run to normalise and rationalise the DB first.