Gender is a grammatical concept, though most people today use gender when they mean sex. In other languages, various endings indicate whether a noun or pronoun is a masculine, feminine, or neuter entity. But in English, gender has pretty much disappeared from English nouns and adjectives. It remains only in the third-person singular of personal pronouns: he-him-his-his for the masculine, she-her-hers-hers for the feminine, and it-its-its for the neuter.
A pronoun must agree in gender and in number with the antecedent (the noun or other pronoun that the pronoun refers to). Thus, a singular antecedent demands a singular pronoun. A problem arises with gender, however. If the noun you're referring to could be male or female, you can get stuck with writing he or she, him or her, she or he, her or him, and so on.
The best solution is this: Make your antecedent plural. Then you can refer back using the plural pronouns they, their, and them—pronouns that do not reveal gender.
Please study the in-depth discussion of sexist writing in the section on Pronouns in Parts of Speech on Grammar.com. Click here for the beginning of that discussion.