You can buy motorbike/car insurance at the border, if you cross into Kazakhstan through a major border crossing. We bought one in 2014 for 2 months for both our bikes, entering Kazakhstan from Astrakhan.
Last summer, we entered via a small border from Russian Altai into Shemonaika (KZ). There, there were no facilities whatsoever, so in the end we failed to buy insurance.
We were never asked for it, as we were never stopped/controlled by the police. The fact we rode small ratty looking bikes, with minimum dusty soft luggage, may have something to do with it. On many occasions the police cars would drive along our side to have a good look at our bikes and us, but they never stopped us.
Insurance is compulsory in Kazakhstan so, if you can buy at the border crossing, just get it. It is also very cheap.
You can read my ride reports (links in my website below). I will also be doing a presentation at the UK HU meeting in June. It will cover all information useful to organise a trip across Russia and the Stans.
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