The Collaborative International Dictionary of English v.0.48:

Directorship \Di*rect"or*ship\, n.
   The condition or office of a director; directorate.
   [1913 Webster]

WordNet (r) 3.0 (2006):

directorship
    n 1: the position of a director of a business concern

Moby Thesaurus II by Grady Ward, 1.0:

133 Moby Thesaurus words for "directorship":
   acme, aedileship, archbishopric, archiepiscopacy, archiepiscopate,
   aristocracy, authority, authorization, be-all and end-all,
   bishopric, blue ribbon, captainship, chairmanship, championship,
   chancellery, chancellorate, chancellorship, chiefery, chiefry,
   chieftaincy, chieftainry, chieftainship, command, consulate,
   consulship, control, convenership, custody, deanery, dictatorship,
   dictature, directorate, dominion, effectiveness, emirate,
   episcopacy, first place, first prize, foremanship, generalship,
   governorship, guardianship, headship, hegemony, height, hierarchy,
   highest, imperium, influence, intendancy, jurisdiction, kingship,
   leadership, lordship, magistracy, magistrateship, magistrature,
   management, managership, masterdom, mastership, mastery, maximum,
   mayoralty, mayorship, metropolitanate, metropolitanship, most,
   ne plus ultra, new high, nobility, overseership, palms, papacy,
   paramountcy, pashadom, pashalic, patriarchate, patriarchy,
   pontificality, pontificate, popedom, popehood, popeship, power,
   prefectship, prefecture, premiership, presidency, presidentship,
   primacy, prime-ministership, prime-ministry, princedom, princeship,
   principality, proconsulate, proconsulship, proctorship,
   protectorate, protectorship, provostry, provostship, record,
   rectorate, rectorship, regency, regentship, rule, ruling class,
   say, seigniory, seneschalship, seneschalsy, sheikhdom, sheriffalty,
   sheriffcy, sheriffdom, shrievalty, sovereignty, stewardship,
   superintendence, superintendency, supervisorship, supremacy,
   suzerainship, suzerainty, sway, top spot, tribunate, vizierate,
   viziership, zenith