You won't need to uninstall it, you just need to enter the key. But keep in mind when you enter the key you will loose any remaining trial days so you may want to wait till your 60 days are up.
I have a screenshot here for a preinstalled HP system. It may be a little different, I think this was NIS 2012.
On the bottom of the main screen, right next to where it shows how many days are remaining, click the word "renew".
It will bring up a screen like this:
You want to click that link that says "I have a key or code to enter".
Then you get a box to enter your key.
Don't enter it now though, click the close buttons to cancell.
It does seem odd that HP would include a paid 15 month subscription as our subscriptions usually come as 1 year or 2 years or 3 years. The free trial periods are usually 1 or 2 months. That would add up to 14 months. I would suggest contacting HP and check with them to see how this is supposed to work. Perhaps they have a special deal with Norton. I am wondering about this product key that is supposed to be for 15 months. You could also check with customer support with the free chat program and ask about that key you have. I have seen other threads in the Forum about HP and 15 month subscriptions, but I haven't seen these threads as solved. Since the instructions don't match what is on your computer, I would check it out.
.Please contact the free chat program by using this link.
If you can't get a satisfactory response from them, then please check it out with HP. I'm concerned about that 15 month key being accepted when the time comes for activation.
Please come back and let us know how you made out. Thanks.
Just ot avoid problems later if you hve technical questions or even about the key -- Is it Norton AntiVirus or Norton Internet Security? My recollection is that HP tends to supply Norton Internet Security so it's important for you to know since the keys are not compatible between different versions.
As Dave says HP does do some unusual subscriptions but if you've a question about using the KEY I'd be inclined to cross check with them but if in doubt don't apply the key until they system starts nagging you about renewing which is usually a few weeks before it expires. Then I'd apply it since that will give you time to sort things out if it misbehaves -- when the subscription runs out there is absolutely no protection any more.