You can still extend the visa if you are already in the UK under the Turkish Businessperson visa. If the business has suffered financially due to COVID-19, the Home Office does have discretion that can be exercised to grant extension where all other conditions are met. This is determined on a case-by-case basis.
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How can Turkish investors continue to live in the UK with the Turkish Businessperson visa?
I've heard that even though the UK Home Office no longer issues new Turkish Businessperson visa, one could still renew it. Is that true? What if my business has suffered a loss during the pandemic?