Most likely you can do nothing about replacing the coax with hdmi
If you have heating a/C ducting in the ceiling, you might pull hdmi thru the duct work
Most likely your best option is hdmi over coax converter
A module goes on each end of the coax
The HDMI signal is converted to digital rf , transmitted over the coax, and converted back to hdmi on the receiving tv end
https://www.google.com/search?q=hdmi+over+coax+converter&oq=hdmi+over+coax&aqs=chrome.1.69i57j0l3.22604j0j4&client=tablet-android-alco&sourceid=chrome-mobile&ie=UTF-8