When you have asked the airport manager for an extra gate, then the airport has been extended with an extra gate the next day.
Go to the office of the airport manager and you will find the gate on the billboard behind him. You can apply for the gate there.
During the day, your competitors can also bid on the same gate, so make sure you are the last one in the office at the end of the day (around 17.45 hrs) and stay there until it's 18.00 hrs and the next day, the extra gate is yours.