The Collaborative International Dictionary of English v.0.48:

Generalship \Gen"er*al*ship\, n.
   1. The office of a general; the exercise of the functions of
      a general; -- sometimes, with the possessive pronoun, the
      personality of a general.
      [1913 Webster]

            Your generalship puts me in mind of Prince Eugene.
                                                  --Goldsmith.
      [1913 Webster]

   2. Military skill in a general officer or commander.
      [1913 Webster]

   3. Fig.: Leadership; management.
      [1913 Webster]

            An artful stroke of generalship in Trim to raise a
            dust.                                 --Sterne.
      [1913 Webster]

WordNet (r) 3.0 (2006):

generalship
    n 1: the leadership ability of a military general
    2: the office and authority of a general [syn: generalship,
       generalcy]

Moby Thesaurus II by Grady Ward, 1.0:

28 Moby Thesaurus words for "generalship":
   arms, art of war, captainship, chairmanship, chivalry,
   convenership, custody, dictatorship, directorate, directorship,
   foremanship, governorship, guardianship, headship, intendancy,
   knighthood, leadership, managership, mastership, overseership,
   presidency, proctorship, sovereignty, stewardship, superintendence,
   superintendency, supervisorship, war