My Dad's board has the same mast attachment system.
In order to be compatible with modern mast extensions, you need what's called a "power joint" and it is an hourglass shaped rubber piece with two threads on either side and is a component of every modern mastbase.
In the one end, you need to screw in a metal piece that will click into your mast-extension and in the other end, you need to screw in a metal piece that will lock into your board.
The former looks like a metal pole with a pointy end and a groove around its perimeter just below the tip. Should be quite easy to identify when you google pictures of windsurf mastbases.
The latter is in principle the same thing but WAY shorter and might be extremely hard to come by...

HiFly used to make those:
www.surfshop-andreas.de/Mastfusszapfen-Windsurfen-Ersatzteil-Hifly-1-Stueck