I think the original question is a bit different from some the replies I’m reading.
It is not about autopilot. It’s about the HSI.
Original question is about “Slaving” the HSI.
This dates back to the olden days steam gauges, where the HSI is just a directional gyro. It does not know the heading - hence the need to “slave” it to the actual heading based on the magnetic compass every 15 minutes or so, since gyros will drift.
As technology evolved, the HSI is slaved to the aircraft heading (which it gets from the flux valve or ADIRS) automatically, or like @Ransom46 is asking by a "sync"hronizing button which must be pushed every say 15 minutes.
From what I know modern aircraft these days don’t need the sync / slave anymore, it’s fully automatic.
Basically from what I know from BMS there is no sync / slave button.
Hope I didn’t go off the mark…