All the singular/plural words have to be in agreement. The key to this sentence is finding the antecedent of who. For example:
There are many celebrities who (?) quite open with their past. (Who refers to celebrities, and thus it is plural and takes the verb: are ) She is one who (?) quite open with her
yes, i think so. Because: she is one of those celebrities (who) is quite open with her past that mean those celebrities are quite open...not her, if you say: she is a celebrity who..."is" will be correct
A plural subject/verb clause would be this: ... who are quite open with their past. Their is plural, so it refers to the plural: celebrities. But that plural pronoun was not in the original sentence. Instead, the original sentence has the singular pronoun, her.