You dont have to, but its a good idea because the paste helps fill in the gaps between the HS and the chip. This will help the transfer of heat from the chip to the HS hense cooler temps.
I read that you can spread it all over the CPU & sink, pull them apart, and scrape all the excess off each with a razor blade. This leaves all the "holes" filled, yet allows maximum metal-to-CPU contact.
That will introduce air into the paste between the CPU and HSF, best thing to do is either use the stock paste on the HSF it if comes with any or use AS5.