Check available kernel version

$ sudo apt-cache search linux-image-5.
...
linux-image-5.4.0-1009-aws - Linux kernel image for version 5.4.0 on 64 bit x86 SMP
linux-image-5.4.0-1009-gcp - Signed kernel image GCP                               
linux-image-5.4.0-1009-kvm - Linux kernel image for version 5.4.0 on 64 bit x86 SMP
linux-image-5.4.0-1009-oracle - Signed kernel image oracle                         
...                            

Check current kernel version in the system

$ uname -r

check available kernel version

$ dpkg --list | grep linux-image

Install specific kernel

$ sudo apt-get install linux-image-5.13.0-27-generic

Activate grub menu

sudo vi /etc/default/grub
...
GRUB_DEFAULT=0
GRUB_TIMEOUT_STYLE=menu
GRUB_TIMEOUT=10
...
set your GRUB_TIMEOUT

$ sudo update-grub

Setup default grub select item

$ sudo vi /etc/default/grub

add the following scripts
GRUB_SAVEDEFAULT=true
GRUB_DEFAULT=saved

$ sudo update-grub

After this setting, the last item you choose in grub menu is the default value.