Few systems propperly account for this
I mean next to no system accounts for leap seconds. In fact it's even impossible to predict when the next leap second will be introduced.
Perhaps the best way would be to leave computers running at a continuous timescale. Something based on "Atom Time" and use something like timezone files to correct for the "propper" wall clock time. This way you would have to update your timezone files anualy, but if you don't, the time your computer displays will be off by a second while the internal time will still be consistent with what the other computers think.
This could probably be retrofited to most computers as they already use pre-made C library functions to convert from "Unix epoch" to local time. Few people do this with their own code, since it's quite a bit of work.