To build a clock that is EXACT, you could have a Cesium isotope 133 based 9192.631770 MHz oscillator. One Second is defined to be 9,192,631,770 cycles of such an oscillator. Thus your clock is EXACTby definition.
However, to build an EXACT Real-Time-Clock, you will need to add a leap-second once in a while. Otherwise your clock will incorrectly gain an extra second once in a while even if it is EXACT second-by-second. Astronomers can tell you when to add the leap-seconds to your Real-Time-Clock, usually at the end of December or June. The last leap-second was at end of June, 2012. There was not leap-second at end of December 2013. It is already announced that there is no need for leap-second at end of June 2013.