The process for renewal is the same as the process for a new passport application with the exception that you will also complete the “Recent Passport” section (SECTION D) of the application form with the old/expired passport details as well as submit the old passport with the renewal application form.

Please see instructions here: https://jamaicanconsulateatlanta.org/how-to-apply-for-a-jamaican-passport/

Further instructions/requirements are available on the PICA website here: http://www.pica.gov.jm/passport-servies/adult-passport-information/renewing-a-jamaican-adult-passport/