Wiktionary
headmistress-ship
n. 1 The position of a headmistress. 2 The tenure of a headmistress.
Usage examples of "headmistress-ship".
Although she had retired from her Headmistress-ship she still exercised a lot of power.
You appear to me to be in full vigour and energy, fully capable of continuing your headmistress-ship for a good many years to come.