Tactical without being disrespectful

Start like it was a new project:
(1) Go through the basic steps of project planning: Scope, Schedule, Cost, Risk (!), stakeholders, ...
For many topics, already loads of material will be available. So it might be faster than starting from zero. On the other side the ammount of material might overextend your capabilities. Get help from the team!

Searching for info in a structured way will help you to get up to speed.

(2) Work to find out where are the biggest deviations between plan/baseline and reality.

(3) Priorize, which topics get your attandence first.

Maybe an important first step:
(0) Accept and communicate, that there will be friction losses due to the handover from other PM. If you follow these steps, you will do the best to reduce the losses.

And one point more:
(x) if you identify some critical points in the project, communicate early.

e.g. "I have analysed the project. Basically its ok. But I see a bigger risk (scedule/cost/...) at workpackage xyz. I do my best to minimize it, and keep you updated on actions and progess."
If you avoid this, it might affect your reputation if some hidden bombs blow off some time later.

Replacing the project management is a calculated risk: Is the risk to the project higher with the previous project manager or with the new one?

Suzi

Without an understanding of the reason why you would replace the PM, then all one can do is speculate, as there are multiple scenarios.

Is the PM 1] leaving, 2] being promoted or 3] are they underperforming. If it is the latter, is it the PM who is seen to be underperforming or are they simply failing to live up to unreasonable expectations?

I have seen many cases where blaming the PM is a plausible way to justify why a project is failing, where in reality it had little chance of such success in the first place. In this case, the PM is used by others to deflect blame and given their marching orders. Often a new one will be parachuted in to replace them. In this scenario check carefully to see if they are handing out parachutes.

The butler did it.

Good feedback from everyone,
however, I think Pankaj seems to give you a practical solution to address this situation

Good feedback from everyone,
however, I think Pankaj seems to give you a practical solution to address this situation

As appointed leader, there are always challenges to win over the existing team. Sometimes this come more easily than other times, mainly due to type of personalities on both ends: PM and team members. Getting to know the team members, building a trustworthy and supporting environment by actively involving the team members and make them feel valued will always help in leveling transition time and overcome challenges.