CentOS

We use 3 Centos systems.
On all 3 systems gives 'cat /etc/centos-release' the result 'Centos Linux release 7.9.2009 (Core)'

On 2 systems gives 'uname -r' the result '3.10.0-1160.108.1.el7.x86_64'
On this 2 systems gives:
'sudo yum update'
the result:
Loaded plugins: fastestmirror
Loading mirror speeds from cached hostfile
* base: mirror.prolocation.net
* epel: mirror.serverion.com
* extras: ftp.nluug.nl
* updates: nl.mirrors.clouvider.net
No packages marked for update


On 1 system gives 'uname -r' the result '3.10.0-1160.102.1.el7.x86_64'
On this system gives:
'sudo yum update'
the result:
Loaded plugins: fastestmirror
Loading mirror speeds from cached hostfile
No packages marked for update

How can I configure this last Centos system that is also download and install the latest kernel and updates?

Is it a long time since you have rebooted? - a new kernel requires a reboot.
Also, CentOS 7 dies in three months time.

A newer kernel than the running kernel is also not available in the directory /boot
The system is now rebooted but "yum update" still give "No new packages marked for update".
Beside this, I had to update the CentOS systems from 7 to 8.

The directory /etc/yum.repos.d contains a file bradford.repo
The bradford mirror contains an older Centos version.
Bradford performs testing before a new CentOS release is placed on the Bradford mirror.
This Bradford mirror is used for FortiNAC from Fortinet.
The cause in clear now.

Beside this, I had to update the CentOS systems from 7 to 8.

There is no supported "upgrade" from 7 to 8. It is a re-install. And in any case CentOS Linux 8 is already EOL, 2 years ago.