When your singular person could be male or female, you have three options:
(1) use their,
(2) use his/her, or
(3) use his with a caveat.
For example:
Each team leader is responsible for their team.
(Using their for a singular is acceptable despite what some might tell you.)
Each team leader is responsible for his/her team.
(This is acceptable, but it's a bit clumsy.)
Each team leader is responsible for his team.
(This is definitely acceptable if all team leaders are male. It's even acceptable if they're not (with a caveat explaining that his means his/her), but it runs the risk of appearing sexist.)
