First off, coolant isn't just coolant. It contains rust inhibitors and antifreeze, for example. As such, ideally it should be changed every few years - in my opinion, probably every 3 years (though I'm now going to be waiting for some troll to say they've not changed the coolant on their car since 1974, and it's fine). So you may well find that the old coolant is now mostly water. Not really somewhere you want to be as you hit winter and sub-zero temperatures (remember the bit about antifreeze in the coolant).

Also, look at how you fitted the new gasket, and took off the old one. You need to ensure that the metal surfaces are clean, so getting off all traces of the old gasket, before fitting the new one. In addition, use a gasket sealing compound.

Further, where did you get the part/gasket from ? If a cheap seller from Ebay, then that is another possible cause for the part/gasket leaking.

So, my advice in total : take off the old part and gasket. Clean the surfaces. Fit new gasket, and sealing compound, and new part. Drain old coolant (make sure you collect it, then dump to drain, don't let it drain out on road/drive, etc). Make up new full-strength coolant mix. Fill, bleed air locks.

(reason for saying careful when draining old coolant : it smells 'sweet' to animals and wildlife. Cats, dogs, hedgehogs, birds, etc will all try to drink/lap it up, and would be poisoned by it)