Once any .link domain is registered, you own it for 1 year period. During this period, you retain the rights to that domain name.

Unfortunately, you can't change your .link domain name once it's registered but you can contact customer support and buy another domain as well as unset the already claimed domain.
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The first domain that you claim will be free of charge for the first year and after that, the price is $12 per year, also each additional domain costs $12.