Probably. If you can determine the actual model reference, we can be certain. MacOS 10.8.5 was from September 2013, and both a a mid-2012 and a mid-2013 MacBook Air can run the current MacOS (10.15 Catalina). However, the next OS (10.16 Big Sur) requires a mid-2013 MacBook Air to run so assuming the MBA in question is a mid-2012, it will be stuck on 10.15.
In fact, it could also be an older MBA (the 11" model started in 2010) which could run 10.8.5 but not 10.15. So please, find out if you can the specific model. E.g. for the mid-2013 MBA, the identifiers are Mid-2013 or MD711LL/A or MacBookAir6,1 or A1465. You can consult https://everymac.com/systems/apple/macbook-air/index-macbook-air.html.