A leap second was recently added on June 30, 2015 23:59:60 UTC.
How are leap seconds implemented on Android (specifically Lollipop)?
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The leap second was not implemented in Lollipop or any other Android version. If you are really concerned with having 'atomic clock' accuracy, use ClockSync, which synchronizes your device's clock with an atomic clock.
If you have root access, this is done automatically. Without root, a countdown assists in you manually synchronizing your clock. That will get you the one second back if you don't have network-provided time.
In Date/Hour Settings page you have a checkbox to enable auto-checking time by the network.
I think it's your mobile operator that gives time. Then the mobile is always up-to-date (time speaking).
I don't think leap seconds are implemented in stock Android if we're not connected on any network.