Senior Partners are rarely hired from the outside and the process is fairly customized to the individual, role, and location. In my case, I was recruited by a search firm and first met with an Advisory Partner and the Hiring Partner on the same day.
A few weeks later, I met with the Office Managing Partner. Once the 3 of them decided to continue the process, I met with Senior Partner leadership across my industry sector (roughly 6 - 8 people) and, ultimately met virtually with the CHRO (although that wasn't their exact title) to discuss the offer, etc.