when assuming a new leadership position how do you balance implementing your ideas and continuity?

If you assume a leadership position in a unit where you feel things aren’t going as they should (not necessarily going to drive the unit into the ground but not operating how you think is best) how do you balance implementing your style of getting the job done and maintaining some continuity. do you feel one can be sacrificed for the other? for example, if you replace a former leader who let things be pretty lax, morale is decent and work is getting done. But you feel efficiency is low for what it could be, and want to change the work environment. any personal examples would be awesome.