It depends on a variety of factors, including the individual's own physiology and psychology, and social and cultural factors.
Some transgender people feel that their sex - the biological characteristics that define male and female - does not match their gender, which is the internal, personal sense of being male or female. For example, a person with a female body may feel like a man.
Some transgender people choose to transition, which means changing their appearance and often their legal sex, to match their gender identity. This may involve hormone therapy, surgery, or both. Others do not transition, or only transition partially.
There is no single answer to whether or not the sex of a transgender person can change. It is a complex question with many possible answers.