The Collaborative International Dictionary of English v.0.48:

Tutorship \Tu"tor*ship\, n.
   The office, duty, or care of a tutor; guardianship; tutelage.
   --Hooker.
   [1913 Webster]

WordNet (r) 3.0 (2006):

tutorship
    n 1: teaching pupils individually (usually by a tutor hired
         privately) [syn: tutelage, tuition, tutorship]

Moby Thesaurus II by Grady Ward, 1.0:

36 Moby Thesaurus words for "tutorship":
   catechization, chair, chair of English, coaching, didactics,
   direction, edification, education, enlightenment, fellowship,
   guidance, illumination, information, instruction, pedagogics,
   pedagogy, preceptorship, private teaching, professorate,
   professorhood, professoriate, professorship,
   programmed instruction, readership, reeducation, schooling,
   schoolmastery, self-instruction, self-teaching, spoon-feeding,
   teachership, teaching, tuition, tutelage, tutorage, tutoring



Bouvier's Law Dictionary, Revised 6th Ed (1856):

TUTORSHIP. The power which an individual, sui juris, has to take care of the
person of one who is unable to take care of himself. Tutorship differs from
curatorship, (q.v.) Vide Procurator; Pro-tutor; Undertutor.