Before you re-apply the thermal paste on your CPU, you should get rid of the old thermal paste from the ends of both the processor and the heatsink.
Dont worry, though; its quite simple.
Youll need:
Microfiber / Lint-free cloth or cotton swab
Isopropyl Alcohol
Replacement Thermal Compound
How To Correctly Apply Thermal Paste To CPU
1.get rid of the remaining thermal paste on the chip.
2.Do this until you get rid of it on the heat sinks end as well
3.Carefully apply a dot of the replacement thermal paste on the CPU when the chip is cleaned and the alcohol has dried.
4.Make sure you carefully place the heat sink back on the CPU after the paste is applied.