I'm not an expert on replacing thermal paste, but I do have a little bit of help to get you started.
First I'm going to disagree with Aadam in that I don't believe you have to remove the motherboard to get to the heat sink. Although iFixit doesn't have a guide that will show you the complete procedure, they do have one showing you how to remove the fan, which is just one step short of where you want to go. So the first thing to do is to follow this guide to the end.
[guide|120426|HP 15-da0012dx Fan Replacement - iFixit Repair Guide]
From there I'm fairly sure all you have to do is remove the four screws holding the heat sink onto the processor and you have the thermal paste exposed.
At this point I'm at the end of my expertise, so I'm going to stop here and leave the rest as an exercise for the student, or perhaps another of our knowledgeable contributors can chime in to complete these instructions.
Although you should in general be okay with just tightening down the four screws, I know from my time at Intel that when I was replacing a processor on a server board, there were very specific torque settings and tightening sequences required for the heat sinks they used. However, keep in mind these were for huge 64 core Xeon server processors so it's unlikely the requirements for a desktop CPU are anywhere near as stringent. If you can find any documentation about replacing the heat sink it would be worthwhile reading through it to see if there are any particular needs.