The short answer is no, as we do not have any evidence to oblige gemstones for Zakat from the Quran and Sunnah. Additionally, scholars have stated that the qualities of gemstones are subjective, making them unreliable as consistent stores of value like precious metals.
Zakat is only payable on zakatable assets. Common zakatable assets are cash, gold, silver, stocks, cryptocurrencies, stocks, and business inventory. Most other assets are not zakatable even if they are high in value. Diamonds and other expensive gems are not zakatable assets. Hence, no zakat would be payable on them. However, if they were bought for the purpose of reselling, they would be considered business inventory and therefore would be considered as zakatable. And Allah knows best.
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