On your Ubuntu server new kernels will will be downloaded regularly, and only get applied when you reboot the server.
To remove old kernel files (as /boot will become full), follow the instructions below:
Open terminal and check your current kernel:
Next, type the command below to view / list all installed kernels on your system.
dpkg --list | grep linux-image
Find all the kernels that lower than your current kernel. When you know which kernel to remove, continue below to remove it. Run the commands below to remove the kernel you selected.
sudo apt-get purge linux-image-x.x.x.x-generic
Finally, run the commands below to update grub2
Reboot your system.