The Collaborative International Dictionary of English v.0.48:

Exert \Ex*ert"\, v. t. [imp. & p. p. Exerted; p. pr. & vb. n.
   Exerting.] [L. exertus, exsertus, p. p. of exerere,
   exserere, to thrust out; ex out + serere to join or bind
   together. See Series, and cf. Exsert.]
   1. To thrust forth; to emit; to push out. [Obs.]
      [1913 Webster]

            So from the seas exerts his radiant head
            The star by whom the lights of heaven are led.
                                                  --Dryden.
      [1913 Webster]

   2. To put force, ability, or anything of the nature of an
      active faculty; to put in vigorous action; to bring into
      active operation; as, to exert the strength of the body,
      limbs, faculties, or imagination; to exert the mind or the
      voice.
      [1913 Webster]

   3. To put forth, as the result or exercise of effort; to
      bring to bear; to do or perform.
      [1913 Webster]

            When we will has exerted an act of command on any
            faculty of the soul or member of the body. --South.
      [1913 Webster]

   To exert one's self, to use efforts or endeavors; to
      strive; to make an attempt.
      [1913 Webster]

WordNet (r) 3.0 (2006):

exert
    v 1: put to use; "exert one's power or influence" [syn: exert,
         exercise]
    2: have and exercise; "wield power and authority" [syn: wield,
       exert, maintain]
    3: make a great effort at a mental or physical task; "exert
       oneself"

Moby Thesaurus II by Grady Ward, 1.0:

33 Moby Thesaurus words for "exert":
   apply, attempt, bring into play, bring to bear, bust a gut,
   do with, employ, endeavor, exercise, expend, go all out, handle,
   make an effort, make use of, manage, manipulate, operate, play,
   ply, practice, push, put forth, put out, strain, strive, struggle,
   throw, toil, try, use, utilize, wield, work