Apt: apt update command fails to update

That means that the public key is not identified as trusted key. You need simply to run the following command followed by the key needed:

sudo apt-key adv --keyserver keyserver.ubuntu.com --recv-keys <pub key>

Maybe it is a problem with your mirror. Even my closest mirror right now is down (ireland). Maybe this issue could be fixed by changing mirror.

You can change the apt source/ repo by and fix this issue by:

$ sudo nano /etc/apt/sources.list

Then you edit the first line by adding a # at the beginning. Add the the end of the line:

deb http://mirror.ox.ac.uk/sites/archive.raspbian.org/archive/raspbian buster main contrib non-free rpi

Your file should look like this:

   #deb http://raspbian.raspberrypi.org/raspbian/ buster main contrib non-$
    # Uncomment line below then 'apt-get update' to enable 'apt-get source'
 #deb-src http://raspbian.raspberrypi.org/raspbian/ buster main contrib $
    deb http://mirror.ox.ac.uk/sites/archive.raspbian.org/archive/raspbian buster main contrib non-free rpi

Then Ctrl-x to save + Y Then :

 $ sudo apt-get update

The issue could now be fixed