Look at astronomical software, e.g. xephem. There will be a "clocks" tab that displays a number of different clocks, TAI (atomic clock, no leap seconds), UTC (global civil time), media solar time (GMT, which ISN'T UTC) and finally, derived from the aforementioned "sidereal time", which is the one you really need to adjust your telescope. Sidereal time is derived from a year with 1 more day basically, because the earth moving around the sun adds 1 more rotation of the background stars. Which is a drift of roughly 4 minutes per day.

https://en.wikipedia.org/wiki/Sidereal_time

Oh, and then there is stuff like Julian date which you need to look up the myriads of catalogues and tables you need for corrections because everything "wobbles" even more than you'd think.

Yes, dropping leap seconds will remove 1 table lookup from the above. But astronomical time systems are so complex that that change is a drop in the ocean.