It will operate its Heathrow route on Saturdays and Wednesdays using an Airbus A321LR aircraft.
Onwards connections are available to Uzbek capital Tashkent and Bishkek in Kyrgyzstan.
Kazakhstan offers visa-free travel for arrivals from the UK.
Passengers must present evidence of a negative PCR test for Covid-19 taken up to 72 hours prior to departure unless they hold a valid vaccine pass.