Is there any word or any rule that we can use instead of writing his/her all the time for possessive determiners
E.g: Student can come with his/her bag. - Student can come with their bag.
Is it grammatically correct if I can write their instead of his/her?
Some schools of thought accept "Singular They," and some (like mine) do not. So it's not a matter of whether it's correct—it's a matter of whether it's correct according to your style guide, review board, grammatical philosophy, etc.
IMHO, the best method is to avoid the problem of gender by pluralizing the entire construction: "Students can come with their bags." Few circumstances don't allow that simple method. English singular pronouns diverge by gender; plural pronouns do not. So going plural removes gender from the equation.
For some while, it was common practice, when gender is not known, to use the male as generic: "A student can come with his bag," not meaning only a male student, but any student. But social values have become sensitive to this practice, and it is in wide disallowance.
