Ok, final resolution: reinstalled the 390... and there's no driver for the current kernel. I did an rpm -ql, and it's for an 862 kernel.
Time to remove, and go to the proprietary (this server has two Tesla cards, and uses CUDA).
Definitely. If you are using CUDA with Tesla cards go straight for the nVidia CUDA repo - it includes the necessary drivers. I presume you know where to look, but for completeness on the list the documentation is at
https://docs.nvidia.com/cuda/cuda-installation-guide-linux/index.html
P.