They as a singular pronoun
Because English does not have a gender-neutral singular personal pronoun (the equivalent of he or she), they, them and their can be used as singular pronouns to avoid the use of awkward constructions such as he/she, him/her and his/her in gender-neutral writing.
Singular usage of they is not new (it has been common since at least the 14th century) and is consistent with spoken language:
The department is looking to appoint a person in their mid-20s.
The mission statement should encompass everyone’s perception of their role.
If you wish to avoid using they as a singular pronoun, there are ways of rephrasing the sentence:
can be replaced with
All staff members should keep their desks tidy.
Every staff member should keep a tidy desk.