The phrase "unexpired portion" refers to the remaining time or duration that something is valid or can be used before it expires or becomes invalid. Full definition
IF MY CAR IS DECLARED A TOTAL LOSS, CAN THE INSURER DEDUCT THE VALUE OF THE WRECK AND UNEXPIRED PORTION OF MY REGISTRATION FROM THE INSURANCE PAYOUT? (insurancelaw.org.au)
Any vacancy occurring before the expiration of the term of an elected member shall be filled by the President's appointment, and such appointment shall be for the unexpired portion of the term. (aaas.org)
If a vacancy occurs in the Presidency, the Vice President shall immediately assume the office of President for the unexpired portion of the term as well as serve the full one - year succeeding term as President. (seismosoc.org)