Update your Dockerfile to have the new package or application version. Rebuild the image and push it to whatever repository you’re using. Update the version tag on the service.
(I hear Jenkins can basically do all of these things when you commit code after it runs your tests with enough configuration.)
You never want to attempt to make a “live change” like this, for two reasons: you’d need to manually make the same change in every replica, and if the system ever decides to scale or relocate and creates new containers and deletes old ones, the new containers won’t have whatever changes you made locally.