The Collaborative International Dictionary of English v.0.48:

Reinsure \Re`in*sure"\ (-sh?r"), v. t.
   1. To insure again after a former insurance has ceased; to
      renew insurance on.
      [1913 Webster]

   2. To insure, as life or property, in favor of one who has
      taken an insurance risk upon it.
      [1913 Webster]

            The insurer may cause the property insured to be
            reinsured by other persons.           --Walsh.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

re-insure \re-insure\ v.
   1. to provide additional insurance for.

   Syn: reinsure.
        [WordNet 1.5]

   2. to insure again by transferring to another insurance
      company all or a part of a liability assumed.

   Syn: reinsure.
        [WordNet 1.5]