Canonical, the commercial arm behind Ubuntu have made the Livepatch Service a few years ago. This allows you to live patch your kernel without rebooting. It works on Linode however it needs some additional configuration. The first thing to do is to change your kernel to Grub2 and reboot your linode. This is well documented here. If you use Digital Ocean it works out the box.
Once you have done this reboot and signup, following the prompts https://auth.livepatch.canonical.com/. You get 3 computers for free as a Ubuntu user. If you need more you need to pay for Ubuntu Advantage. Once you login you will get the install scripts to set it up. Run them and your good to go.