ostanak

1. staying on, not leaving; keeping one's place or position
   Odlučio se za ostanak u Srbiji uprkos ponudama iz inostranstva. — He decided to stay in Serbia despite offers from abroad.
   Tim se bori za ostanak u ligi. — The team is fighting to avoid relegation.

Ostanak is the act of staying on rather than leaving (ostanak u ligi, ostanak na vlasti); a period spent somewhere is boravak. Do not confuse with ostatak “remainder”.