Source : Webster's Revised Unabridged Dictionary (1913)

Tutorship \Tu"tor*ship\, n.
   The office, duty, or care of a tutor; guardianship; tutelage.
   --Hooker.

Source : WordNet®

tutorship
     n : teaching pupils individually (usually by a tutor hired
         privately) [syn: {tutelage}, {tuition}]