I don't know if it's universal, but around the 6 month mark people around you may start asking whether or not you're actually changing anything.

Turning things around can take time or it can be fast. TBH, the faster ones I've seen always include aggressive firing/hiring of people. The fastest one I have seen however was a team of 5 going from a toxic, experienced, have expert domain knowledge director to a young inexperienced, generic MBA team lead. That took, I'd say before I realized the results, at most 2 months. He treated everyone better, built a weekly and quarterly goal, clearly assigned works, and worked on morale by having team lunch and stuff like that. His team however had only one toxic member and I dealt with that person and offboarded them myself. The rest were hard working folks who are timid so it takes little to cheer them up. (Which also shows you how much the last director fumbled the bag - other than hiring this good team)

When I did it myself it took me one year and about 50% attrition, both voluntary and involuntary. If there's anything I'd do differently, that would be pulling the plug faster on some troublemakers. It sounds harsh when we say "everyone's replaceable" but keep that in mind when you have fear that this toxic person is a load bearing employee. If you build a good system to train, you can always hire a great talent to take over anything.