1. Tell your team that cleaning up the tech debt is a major company priority, and even if some mistakes are made along the way, that's an acceptable price to pay for the benefits involved. People shouldn't let the fear of breaking something, dissuade them from cleaning up the mess.
2. Have your team invest heavily on building test/QA infrastructure, so that if they were to break something, it would get automatically caught and flagged, before it reaches production. If the advice given in bullet 1 scares you, then you need to double down here to make up for it.
I've been in teams where pull requests that significantly cleaned up the code base were literally rejected, because people were paranoid that any change at all could break something in unforeseen ways. People just bunkered up into a "if it ain't broke, don't touch it" mentality, which meant that the tech debt problem never ever improved. Ultimately, the only way to get yourself out of this hole, is by encouraging people to take risks even if it involves them sometimes failing, and building better safety nets to catch them on the occasions when they do fail.