Ok. So if you have the infra already, it's really just a matter of actually writing the tests. That can be done incrementally.
40%-60% unit test coverage is honestly not too bad. But if the company's bottom line rests on this code, you probably want to get that up. 100% though isn't really worth it for application code, but it is definitely worth it for library code.
One thing where I work is that all commits must be reviewed before being merged. A great way to improve coverage is to be that guy when people send you PRs.