"Overdue premiums" refers to insurance payments that have not been paid by the due date. It means that someone has not paid their insurance premiums on time, and these payments are now considered late or overdue. Full definition
As the time passes, process becomes tough and you may also need to pay overdue premiums along with interest and additional documents, which could include medical tests also. (policybazaar.com)
Many policies also have an «automatic premium loan», provision that is activated to pay overdue premium. (newyorklife.com)
When a policy has lapsed, it can be revived and brought to its full force by payment of overdue premiums (with interest) and a declaration about state of health or fresh medical examination. (tomorrowmakers.com)