Clean the old thermal paste both from the cooler and the CPU. It is best to use isopropyl alcohol and cotton swabs or paper towel, but be careful not to go too hard on the CPU.

Dont use too much thermal paste, just enough to cover some portion of the pad. If you have a spreader, use it. The thermal paste will apply evenly after you tighten the heatsink. It is good to replace the thermal pad as well, but not mandatory if it is still good.

You can also open the fan itself and clean it further if necessary.

Once you have opened the laptop, it is a good idea to upgrade the RAM or the SSD if you want.

It is also recommended to use compressed air to remove any dust in the laptop and the fan.