NRS 450.110: Vacancies.

Except in counties where the board of county commissioners is the board of hospital trustees, a vacancy in the board of hospital trustees occasioned by a resignation, removal or otherwise must be reported to the board or boards of county commissioners and must be filled in the same manner as the original appointment. An appointee shall hold office:

1. Until the next following general election in the usual manner; or

2. If the appointee is a physician appointed to fill the vacancy of a member appointed pursuant to the provisions of paragraph (b) of subsection 5 of NRS 450.090, for the unexpired term of that member.