Why does my MacBook Air come up with error when installing macOS Sierra

It is definitely a good idea to perform your own clean install of an OS when acquiring a used computer.

How are you booting the macOS installer? Recovery Mode, Internet Recovery Mode, or bootable macOS USB installer (how was the installer created)?

It is best to erase the whole physical drive as GUID partition and MacOS Extended (Journaled) before selecting "Install macOS".

Bad WiFi or Internet connections can contribute to issues, as does using an out-dated installer, or using a bad USB stick.

Thank you for the information. What might be happening is that you are booting into the local recovery partition which may be using a version of Sierra (or Sierra installer on the local recovery partition) with expired security certificates. Apple updated the security certificates for the installers a year or two ago which may be why you are getting this error. You can try setting the date back to sometime in 2016 (maybe 2017) and trying local recovery mode again. If you can no longer boot into macOS to change the date, then you can do so using the Terminal app located on the "Utilities" menu when booted into the macOS installer using the following command to change the date to Jan. 1, 2016 and time of 22:33 (aka 10:30pm) :

date  -u  0101223316

Here is an article explaining how this command works and how to format the date and time portion:

https://bensmann.no/changing-system-date-from-terminal-os-x-recovery/

Or you should be able to access Internet Recovery Mode using Command + Option + R to access the current online installer. Depending on the exact model of your MBAir, this may give you High Sierra, Catalina, or possibly even Big Sur. This will bypass any outdated certificates plus you should get the most recent version of macOS supported by you laptop (in theory because sometimes this option will only access the original version of macOS which shipped with this laptop from the factory -- still a good option since then you can upgrade to a later version of macOS as a second step).

If you access the macOS 10.13+ installer, then to erase the whole physical drive you will need to first launch Disk Utility from the installer, then click on "View" and select "Show All Devices" so that the physical drive appears on the left pane of Disk Utility. Erase the whole physical drive as GUID partition and APFS (top option). Quit Disk Utility and select the "Install macOS" option.

If you end up with the macOS 10.11 El Capitan or macOS 10.12 Sierra installers, then the physical drive is visible by default within Disk Utility. However, you still need to erase the physical drive but as GUID partition and MacOS Extended (Journaled).

If you end up with a macOS 10.6 - 10.10 installer, then you need to partition and format the physical drive as described in this article:

https://www.owcdigital.com/assets/support/support-formatting-and-migration/Mac_Formatting_6-10.pdf