Does project manager(PM) have any role to play in large scale projects developed under Scrum framework? Consider that multiple scrum teams will be executing the project.
No "Project Managers" in Scrum
There is no "project manager" role defined by the Scrum framework. The only three roles are:
- Product Owner
- Scrum Master
- Development Team member
Any other roles your organization may have exist outside the Scrum Team. If you add or remove roles from a Scrum implementation, the result is not Scrum.
Well, there is no single mechanism to scale Scrum. But most popular frameworks, being it "LeSS" or "SAFe" or "Nexus" don't have a project manager role, because that role is not in Scrum and does not follow the Scrum mindset. The scaling frameworks try to transport agile to a higher level, not cut it off and replace it with traditional styles at a certain level.
So no, in a real agile company there is no place for a project manager because that is not how agile works. If they are willing to adopt to the agile style however, I'm sure there are positions that might be a good fit for former project managers. But it should be seen as a job change, because it is.
I'm going to answer a little differently by pointing out some examples of Agile working at scale (not necessarily Scrum).
Microsoft put out a really good video on how they implement Agile for their on-going development of the Visual Studio product. It might be worth the ~45 minutes of your time to watch, because you can pick up on a lot of practical things that they do to coordinate this massive product across many feature set teams (800 people total). Microsoft Visual Studio Product Development Video
Another example is Eric Brechner talking about XBox and Agile project management on the XBOX team for a talk at Google: Google Talks: Agile Project Management with Kanban
Google has a lot of examples over time - going back to 2011 and 2012 at a minimum. Example: Google PM on Software Product Management NOTE: Also the Objectives and Key Results (OKR) literature from Google gives you a really visceral feel for how Google manages from the CEO on down
Basically - my recommendation is to read it all, but then find case studies of companies and teams that have implemented at scale.