i think that's a job for a professional jeweller/ watch repairer. I'm guessing that they would need to uncurl the link ends (by heating up?) in order to remove then doing the same to the next link to reattach it to the bracelet. Doesn't look like something you could do yourself, unless you had the tools and confidence to tackle it yourself.
Might be worth getting the opinion or advice of a professional before you do anything.