The promise that Mrs. Drover made to her fiancé is never made explicit. However, it is possible nonetheless to determine what it might have been. As the young man is about to leave Kathleen and head for the front, he implies that the two lovebirds have made a promise to each other:
"I shall be with you," he said, "sooner or later. You won’t forget that. You need do nothing but wait."
As Kathleen doesn't respond to this, one can only surmise that she's tacitly promised that she will wait for her lover to return, come what may. But it isn't very long before she regrets making such an "unnatural" promise, which though it has strengthened the bond between Kathleen and her lover has isolated her from the rest of humankind. As soon as her fiancé has departed, Kathleen feels hopelessly lost all of a sudden. She also feels the crushing burden of the promise that she's made.