Replacing a 1963 GE 125 Amp, 240V service panel
Find a GE distributor in your area and have them order you a new INTERIOR for whatever their current product line is that matches your needs. The box dimensions haven't changed enough in 40 years to be a problem, a new interior (and cover) should drop right in. 

You also have what's called a "split bus" installed there; the lower section of the panel is protected by a breaker in the upper section. There are two main reasons for this, one of which is not in play here, the other of which is something you need to determine if it applies. 

The main reason for a "split bus" panel is to take advantage of what's called the "6 hand rule" meaning that if a firefighter needs to kill all power in your building, they only have to move their hand 6 times. So when a panel doesn't have a "Main Breaker" (as yours doesn't), then the top 6 spaces are all supposed to be 2 pole breakers, and one of those 2 pole breakers then feeds the bottom section where all the single pole breakers are. Your setup already violates that, you have 10 handles up top. Maybe that's because it has been changed by someone who didn't understand, who knows but that is already a violation if that was the original reason.

The other reason for doing a split bus is if you have a backup generator (or now a Solar Power system) in which you only want to power SOME of the loads when under the backup source. That too does not appear to be the case here because that typically needs to have some sort of interlocking system to isolate the unwanted parts of the system when connecting that backup source, and I don't see anything like that. But only you can tell for sure.

So in all likelihood you can get a more standard GE panel interior with enough spaces (20) and that will fit in that box. If it were me, I would get one with a Main Breaker now rather than rely on that 6 hand rule issue and trying to rearrange all of the circuits so that there are only 6 breakers on the upper half, but you may not have enough physical space in the box for that. If that's the case, you may just need to change out to a new box too. But GE has not changed the breakers themselves, so by sticking with GE you can re-use those and save yourself some money.