NOUN (3)

1. a bishop in one of several Eastern Orthodox Churches in North America;

2. a bishop in eastern Christendom who holds a place below a patriarch but above a metropolitan;

3. a viceroy who governed a large province in the Roman Empire;

The Collaborative International Dictionary of English v.0.48:

Exarch \Ex"arch\, n. [L. exarchus, Gr. ? ? commander; ?,?, out +
   ? to lead, rule: cf. F. exarque.]
   A viceroy; in Ravenna, the title of the viceroys of the
   Byzantine emperors; in the Eastern Church, the superior over
   several monasteries; in the modern Greek Church, a deputy of
   the patriarch, who visits the clergy, investigates
   ecclesiastical cases, etc.
   [1913 Webster]

WordNet (r) 3.0 (2006):

exarch
    n 1: a bishop in one of several Eastern Orthodox Churches in
         North America
    2: a bishop in eastern Christendom who holds a place below a
       patriarch but above a metropolitan
    3: a viceroy who governed a large province in the Roman Empire