Yes, travel insurance is a sensible default for a trip to Osh, and especially so if trekking in the Pamir-Alay range is part of the plan. Osh functions as Kyrgyzstan's southern gateway into the Alay Valley, and that terrain - high passes, remote trails, and thin phone coverage - is where a routine city stay turns into one that genuinely needs evacuation cover. Travelers passing through only for the bazaar and city sights still benefit from standard medical and trip-disruption cover, since Osh's own airport connections can be limited outside the main season.
Osh has regional hospital care for routine issues, but complex or serious cases are often referred on to Bishkek, the capital in the north, with international evacuation sometimes required for anything beyond that. Confirm your policy explicitly covers transfer between Kyrgyz cities and, if needed, evacuation abroad, since a policy that only reimburses local clinic visits misses the step most likely to involve real distance and cost for a trip based in the south of the country.
Trekking into the Alay Valley and the wider Pamir-Alay range is the genuine draw for many visitors flying into Osh, and it carries real risk from altitude, weather that shifts quickly at elevation, and trails far from any road. High mountain passes in this range are generally only reliably open during the summer trekking season, roughly June through September, with snow closing many routes outside that window. Confirm your policy names high-altitude trekking specifically rather than assuming general hiking cover applies once you are above the valley floor.
Keep any clinic paperwork, guide or permit records, and receipts for transport or equipment loss, since claims involving mountain routes out of Osh tend to need more documentation than a routine city illness. Check whether your existing health cover extends abroad and specifically to Kyrgyzstan before relying on it, and confirm the claims process in your policy wording before you head into the Alay Valley rather than after an injury has already happened far from a road.