However, I previously bought a 3-PC licence and it still have one available for PC (and will only expire in 6 months). How can I use this available licence to replace the NIS on my laptop (which is expiring in a few days time)
On the trial version it should be enough to click on Renew at the bottom of the main screen of Norton and enter the KEY that you purchased.
However it may ask you to create MyNortonAccount if you have not already -- this is not a marketing thing but keeps track of your Norton products, their KEYs and the number of activations so please set that up. Or if you have already set it up then just point to it and log in ....