Also, what are your new system specs...PSU you're trying to save, motherboard, CPU, GPU. I assume you know it's not a full modular PSU else you'd just go to find a replacement system cable for it. If not modular it may be low-spec enough to not be worth repairing for the new system. That's why knowing full specs will help.
Otherwise it's definitely possible to solder on a new 24pin connector. Just cut that one off then cut one off a scrap donor and solder splice the wires together. Or
crimp splice, either way works. But it may be salvaged another way...so pics would help.