You could try creating another IK handle on the disconnected joint and parenting that to the root. That should keep it in place. If that doesn't solve your issue, look up tutorials on rigging fingertip IK, those should have a similar enough setup to get you on the right track
Sorry to bother... but the main problem I have now is that I can't keep the end of the chain connected to the root (to the watch bone) so It doesn't move along with the Ik handle or when I rotate the clasp bones. Any idea?
You could try it like this: The red parts are your main bones. The watch face bone should be the root bone. From the root, you'll have one joint chain (Blue) going down towards the second bone - look up a spine rigging toturial if you're not sure how to set that up. From there, you'll have two bones controlling each part…