All travelers over age 10 except merchant seamen and airline crew must have a travel authorization completed 72 hours before departure, and a medical certificate with a negative PCR test for COVID-19 from within the last 5 days before arrival in the Turks and Caicos Islands. They must also have proof of health/travel insurance with COVID-19 cover (including cover for any necessary in-country medical treatment, quarantine costs or repatriation/medevac) and must complete a health screening questionnaire.
Children under the age of 2 are exempt from presenting a COVID-19 test.
Travelers with proof of recovery from the virus within the last 90 days prior to boarding. Proof of a recent positive viral test and a letter from your healthcare provider or a public health official stating that you were cleared to travel.
More info at the CDC site
Travelers who did not get tested, are advised to stay home and self-quarantine for 10 days after travel.