Source : Webster's Revised Unabridged Dictionary (1913)

Reinsure \Re`in*sure"\ (-sh?r"), v. t.
   1. To insure again after a former insuranse has ceased; to
      renew insurance on.

   2. To insure, as life or property, in favor of one who has
      taken an insurance risk upon it.

            The innsurer may cause the property insured to be
            reinsured by other persons.           --Walsh.

Source : WordNet®

reinsure
     v 1: provide additional insurance for
     2: insure again by transferring to another insurance company
        all or a part of a liability assumed
     3: insure again by assuming all or a part of the liability of
        an insurance company already covering a risk