If a person has fallen far behind with recommended COVID-19 vaccination, do we ever need to re-start the vaccine series?

No. Simply administer the next dose that is currently recommended. To determine what is needed now based upon a person’s vaccination history, age, and immunocompromised status, refer to the CDC COVID-19 Vaccination Infographic (for most people):

www.cdc.gov/vaccines/covid-19/downloads/COVID19-vaccination-recommendations-most-people.pdf, or the CDC COVID-19 Vaccination Infographic (for immunocompromised people): www.cdc.gov/vaccines/covid-19/downloads/COVID19-vaccination-recommendations-immunocompromised.pdf.