How would you resolve conflict between very senior leaders?

"This role was pretty niche and felt like a mix of chief of staff and TPM supporting a really large engineering organization. The process was recruiter screen, then the hiring manager, then a team screen with peers, then conversations with the engineering directors I would support and their managers. It was a lengthy loop and most of it was behavioral or simulation based. There were not many technical components to it and it was not really a case interview. The whole thing was much more about how I would operate inside the org than about technical depth."