HONG KONG—TikTok, the buzzy short-video platform owned by Chinese technology giant Bytedance Ltd., said it would pull out of Hong Kong within a week in light of “recent developments” in the city.

Last week, mainland Chinese authorities imposed a fast-tracked national-security law on Hong Kong that includes provisions empowering police to order internet companies take down content deemed threatening to national security. TikTok will pull its apps from Google and Apple app stores in the city and cease operations for existing…

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