A pronoun must agree with its antecedent in person number and gender?

Yes, a pronoun must reflect the person, number, and gender of its antecedent:

The person of an antecedent is:

• first person (the person speaking)
• second person (the person spoken to)
• third person (the person spoken about)

The number of an antecedent is singular or plural;

The gender of an antecedent is male, female, or neuter;