The Collaborative International Dictionary of English v.0.48:

Primacy \Pri"ma*cy\, n. [LL. primatia, fr. L. primas, -atis, one
   of the first or principal, chief, fr. primus first: cf. F.
   primatie. See Prime, a.]
   1. The state or condition of being prime or first, as in
      time, place, rank, etc., hence, excellency; supremacy.
      [R.] --De Quincey.
      [1913 Webster]

   2. The office, rank, or character of a primate; the chief
      ecclesiastical station or dignity in a national church;
      the office or dignity of an archbishop; as, the primacy of
      England.
      [1913 Webster]

WordNet (r) 3.0 (2006):

primacy
    n 1: the state of being first in importance

Moby Thesaurus II by Grady Ward, 1.0:

133 Moby Thesaurus words for "primacy":
   abbacy, accent, acme, archbishopric, archdeaconry, archiepiscopacy,
   archiepiscopate, ascendance, ascendancy, authority, authorization,
   balance of power, be-all and end-all, bishopdom, bishopric,
   blue ribbon, canonicate, canonry, cardinalship, championship,
   chaplaincy, chaplainship, command, concern, concernment,
   consequence, consequentiality, consideration, control, curacy,
   deaconry, deaconship, deanery, deanship, directorship, dominance,
   dominancy, domination, dominion, effectiveness, eminent domain,
   emphasis, episcopacy, episcopate, excellence, exquisiteness,
   first place, first prize, headship, hegemony, height, high order,
   high rank, highest, imperium, import, importance, influence,
   interest, jurisdiction, kingship, leadership, lordship,
   magnificence, management, mark, marvelousness, mastership, mastery,
   matchlessness, materiality, maximum, merit, moment, most,
   ne plus ultra, new high, note, overlordship, palms, paramountcy,
   pastorate, pastorship, peerlessness, power, prebend,
   prebendaryship, precedence, predominance, predominancy,
   predomination, preeminence, prelacy, prelateship, prelature,
   preponderance, prepotence, prepotency, presbyterate, presbytery,
   presidency, principality, priority, record, rectorate, rectorship,
   rule, say, self-importance, significance, sovereignty,
   splendidness, splendiferousness, stress, superbness, supereminence,
   superexcellence, superfineness, superiority, supremacy,
   suzerainship, suzerainty, sway, top spot, unsurpassedness,
   upper hand, value, vicariate, vicarship, weight, whip hand, worth,
   zenith