I just started using ArcGIS Pro and just migrated an MXD over to Project File at work. I notice that it is pretty slow to draw on our network. If I move the project file to my local C drive.. it's a bit faster. Any clue why it is slow to draw on our network?
Did you check if the computer that you have run ArcMap on can handle the higher standards of Pro?
Have you tried building the project from scratch in Pro instead of importing an mxd?
What data formats are you using? Shapefiles, file geodatabase, Enterprise geodatabases? Is the data stored on your network or on disk? Are you using a VPN to get network access? Using Citrix?