Can anyone maybe provide how this website can be sped up?
MAGENTO 1.9FULL PAGE CACHE
CLOUDFLARE - CACHE/DEFER JS/ETC
EXT/PLUGINS DISABLED WHICH AREN'T USED
I ran the site through GTmetrix and there are a few recommendations that you can follow:-
What Full Page Cache are you running?
I can see that you are running PHP 5.6? You may want to consider switching to a newer PHP version (if all of your extensions support it) as they perform better and uses less resources.
If you are running a version older than 1.9.4, here's the official patch for PHP 7.2 support:-