Looking more closely at your photo and responding to the other comments.
The thing that the baby blue arrows are pointing to has come loose and created the gap that the red arrow is pointing to. The tailpiece needs to be removed so that it can be glued back into place with hot hide glue. Not a big deal, had it done on my bass last month in fact. It does need to be done correctly.
The purple arrow points to the endpin fixture and looking more closely it is also pulling loose as indicated by the orange arrow (and maybe someone tried to fix that with blue painter's tape in the past?) You have options here, but it needs to be properly reseated and I think that you were asking about being able to extend an endpin, which you definitely should want and need to do. I didn't know about the removable wooden Kay ones, having one made might be an option. Wood is my personal favorite endpin material. Depending on the story of this bass and what you want to do with it, as someone else suggested it's worth considering replacing the whole fixture with a modern endpin assembly, which would be raised to whatever height you need for it to be and lowered into the body of the bass when you're moving it around town.
I would also personally be inclined to replace that tailpiece wire with something different, but I'm not a Kay guy and one of our resident Kay experts would have information on whether or not that's advised on Kays.
Comes back to: Is it your bass or something you're considering buying? Are you trying to historically preserve it or make it into a reliable working instrument?
If this is something that you are considering buying, these issues are fairly "routine maintenance/repair" type issues, nothing that should chase you away. It would be good to get a look at the neck joint, fingerboard and pegbox as well, those are areas that can be more seriously problematic. That said, Kay basses are worth saving and can be very good working instruments, depending on what you're going for.
