How can a project manager survive in this VUCA world?

A skill that have always proved to be successful, assertiveness! Require scope, budgets and timelines and do your best to hold your teams to them.

VUCA has always been there. It has manifested in different ways and in different proportions, but has always been part of the PM process. Careful analysis of the environment to determine where VUCA manifests is part of the job -- it is that analysis that will always allow you to thrive as a PM, irrespective of circumstances. It is important to remember that trying " to be on schedule, within the budget without any scope creep" is not a recipe for rigidity of planning or process, but a goal to seek through active and recurrent management.

great question! may I offer these?

1. High energy level
2. Attention to detail

Oh yes.....well said Michael....assertiveness !!

The only way, in the extremes, to survive in VUCA environments is to have a project manager. The problem is some project managers do not understand that people pay for prevention, not for cure. The first problem is the definition of project manager you find inside organizations is not the right one. But when organizations hire project managers, from 1956 up to date, is just to work in prevention mode what is actualy named VUCA.