Ask HN: How to improve code quality at a new job?

I recently was hired to a new position as a senior developer (probably in the upper 1/3 of seniority) and found that their code quality is kind of abysmal. The code base is pretty sizable and has a bunch of issues: one giant project with all the code in it, very few unit tests, 15 levels of interfaces for single objects, stuff like that. I want to bring it up to my boss and try to push the team toward better practices but I'm not sure what the right way to do this is. I'm not sure whether it's from a lack of knowledge on the part of the team or an old cold base that they just keep iterating on. It's not really feasible to suggest they stop doing new work in order to fix all these problems. Does anybody have experience in a situation like this? What's the right way to push overall code quality in the right direction?