As Jive Turkey said, headsets are sold complete including the crown race. The only extra thing you might need are spacers in case the stack height of the new headset is shorter than the original. The flip side, a taller replacement than the original can be more problematic if the fork is too short.
One thing to check is that it's compatible with your frame and fork. Most bikes sold in the USA take ISO headset - 1"x24tpi thread, 30.2mm headtube, and 26.4mm crown race. However a number of bikes are JIS, meaning the headtube and crown dimensions are 30.0, and 27.0mm respectively. As I remember Specialized bikes, among others, were JIS for a number of years, so unless you have a Specialized the odds favor ISO, buty it's something to be aware of.
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