you should clean it with a soft cloth and rubbing alcohol to remove the old stuff, then apply a small amount of new thermal grease, you dont need much as it squishes and spreads out to cover the whole CPU. Removing the old stuff first ensure good contact which will give you better performance.
This might be a good opportunity for you to polish (lap) the base of the new heat sink - leave the CPU alone. I polished the base of my HS and obtained a 5 deg to 8 deg drop in temps (running similar apps).
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If you put no thermal paste at all and just have metal on metal contact you will only get a small fraction of the heat transfer capabilities because of all the air gaps, your CPU will overheat and either shut down the system or die. Putting the new stuff over the old stuff will give you better than none at all but still not good, it will take slightly longer but your CPU will still overheat fairly quickly.