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It depends where you live. Fitbit's warranty runs for 2 years in Europe but only 1 year elsewhere.
If you are still covered then you can contact customer support to see if they will replace it:
If you are out of warranty then your options are limited. Although not designed to be replaced by users there are replacement straps available on amazon, eBay etc but you need some DIY skills to fit them (there are tutorials on YouTube).