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The closest airport to Kaarli Kirik is Tallinn Airport, which is located in Tallinn. If you plan on visiting or staying in this area, landing at Tallinn Airport will be your best bet.
The cheapest flights to Estonia recently found by momondo users are $11 with Ryanair, $25 with Wizz Air UK, and $48 with airBaltic.
Estonia has relaxed its travel restrictions. As well as Estonian, Latvian, and Lithuanian nationals/residence permit holders and foreign citizens with family members in Estonia, travelers without symptoms of COVID-19 who are arriving from an EU Member State, Schengen member state or the UK may now enter Estonia. A 14-day quarantine applies to travelers arriving from all countries except those in which the COVID-19 infection rate is 16 cases or fewer per 100,000 people for the previous 14 days. A list of countries from which arrivals are not required to self-quarantine is available on the official government crisis website. As of August 24, travelers arriving from the UK are required to self-isolate for 14 days. If you are planning to travel to Estonia at this time, it is recommended that you stay up to date on current restrictions and follow proper safety measures while in public.