If you are running a local DNS server like named/bind and don't want to use the ISP supplied DNS servers that are announced via a DHCP request (using dhclient) then the solution is simple.
The reason should be obvious, but normally running your own DNS server will provide a more reliable, and fast DNS response and you won't have to worry about filtering as much (unless your upstream filters or proxies outgoing DNS requests).
Add the following line, or in many cases you can find the line is there but just commented out with a #. Uncomment it or add the line like below:
prepend domain-name-servers 127.0.0.1;
Need more DNS servers just add a comma after:
prepend domain-name-servers 127.0.0.1, 192.168.10.80;
Now when checking /etc/resolv.conf, you should see that the first DNS server is 127.0.0.1 and then whatever your ISP or LAN provided you with.
Instead of the "prepend" option, we can use "supersede" which will completely ignore all the DNS servers provided from the DHCP server.
Add the following line, or in many cases you can find the line is there but just commented out with a #. Uncomment it or add the line like below:
supersede domain-name-servers 127.0.0.1;
Just like the prepend option you can specify multiple DNS servers like this:
supersede domain-name-servers 127.0.0.1, 192.168.10.80;
Of course, keep in mind that if your local DNS fails or is not working or starting for any reason, that DNS requests will fail, which will generally cause many things to break. It is probably wise to use a secondary, trusted DNS server on your LAN or on the public internet if possible.
On most GUI Linux's such as Ubuntu/Mint etc.. you will have systemd-resolved which has it's own listener on port 53 which forwards requests to the actual DNS server (eg. your ISP's). This will conflict with your local listener (eg. bind/named). If you want to use your localhost DNS successfully remember to disable systemd-resolved and stop the service or you will have broken DNS.
systemctl disable systemd-resolved
#
remember to stop it too!
systemctl stop systemd-resolved
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