An opening gambit might be "I can no longer afford our romance."
"This is a first step, an opening gambit to get a handle on the problem."
But the are you new in town question was a standard opening gambit.
The opening gambit to politely asking him to move on?
The opening gambit was on its way, but it would not be the main purpose of the meeting.
But then his remark had simply been in the nature of an opening gambit, anyway.
He decided that the best opening gambit was simply to tell them his name.
But I believe this is just an opening gambit in a much larger game.
This is the opening gambit and not the end game.
If the change of rooms had been the opening gambit, so much the better.