nastupiti

1. to perform; to appear; to play
   Bend je sinoć nastupio na Exit festivalu. — The band performed at the Exit festival last night.
   Prvi put je nastupio za reprezentaciju. — He played for the national team for the first time.
2. (of a period, state) to set in; to begin
   Posle svađe je nastupila tišina. — After the argument, silence fell.
   Nastupila je zima i putevi su zaleđeni. — Winter set in and the roads are icy.
3. (with an adverb) to act; to take a stance
   Direktor je na sastanku nastupio vrlo oštro. — The director took a very hard line at the meeting.

It does not mean "to step on" something — for that Serbian uses stati na.