You may be surprised to find that the following sentence, after decades of being considered nonstandard, is now considered standard in American written English.
Standard
Every semester, a student leaves the class without their umbrella.
Here, the new third-person singular pronoun “their” refers back to the singular word “student.”
This used to be considered an agreement error, but both the Chicago Manual of Style and the American Psychological Association have changed their standards.
Other standard ways of expressing the idea in the sample sentence above include substituting “his or her” for “their” or by making the word it refers to plural so that it agrees with the plural pronoun. The Chicago Manual of Style prefers these uses in formal writing:
Standard (Formal)
Every semester, a student leaves the class without his or her umbrella.
Standard (Formal)
Every semester, students leave the class without their umbrellas.
The subjective case pronoun they can also be used with a singular antecedent:
Standard
If someone wants to join the club, they need to bring a check for five dollars.
In the sentence above, the singular indefinite pronoun someone is paired with the singular subjective case pronoun they. If necessary, this can be re-written in a number of ways, some more awkward than others:
Standard (Formal)
If someone wants to join the club, he or she needs to bring a check for five dollars.
Standard (Formal)
If someone wants to join the club, that person needs to bring a check for five dollars.
Standard (Informal)
If you want to join the club, you need to bring a check for five dollars.
Standard (Informal)
If people want to join the club, they need to bring a check for five dollars.
All of the above are correct, but the first two are more formal and the last two are more informal. Consider your audience as you consider your use of pronoun / antecedent agreement.