superintendentship
/ˌsuːp(ə)rɪnˈtɛnd(ə)ntʃɪp/ /ˌs(j)uːp(ə)rɪnˈtɛnd(ə)ntʃɪp/noun
1The office, position, or role of superintendent; supervision or charge of some activity, person, organization, etc.
2An instance of this; a position or period as a superintendent.
Origin
Mid 16th century (in an earlier sense). From superintendent + -ship.