Quote - On A Promise

In British English, "on a promise" simply means that you have arranged to or at least expect to have an intimate encounter with someone - usually your regular partner.

I can never understand why, when your date said to pick her up at a specific time, you have to wait another half an hour before she is ready.

Doc, wonderful !  Love the drape of the blankets.  Where did you find that, if I may be so bold, sir?