That’s an interesting question because it’s not as clear cut as it used to be. Directors are appointed for a four year term but can be removed by the Governor at any time for cause. California Food and Agriculture code covers State owned fairgrounds like the Orange County Fairgrounds. If the link doesn't work, go to the Food and Agriculture code and find section 3960.
FYI - We call it a fairground but the State calls it the 32nd District Agricultural Association or 32nd DAA.