nice - Change niceness (priority) of a running process

Is it possible to set a new nice level of a running process with a known id?

Does this operation require root access, or just being the owner of the process?

If you're at a terminal you can use renice

renice [-n] priority [[-p] pid ...] [[-g] pgrp ...] [[-u] user ...]

A simple example would be

renice 8 31043
31043: old priority 5, new priority 8

You can also pass it hard flags, but it follows that order (you have to pass priority first and then the pid - if you change the order it will show the usage messagge)

renice -n 5 -p 31043
31043: old priority 8, new priority 5

Priorities work on a scale of -20 to 19 - The lower the number, the higher it's priority on the system.

If you own the process then you won't need root - however, if the process is owned by another user or if you plan on changing the group/user of the process root (via sudo) will be required.