A tertiary beneficiary is another term for a third beneficiary who would be paid as default in the event the primary and secondary beneficiaries have died or do not qualify per specific instructions written.
For example:
Primary beneficiary: 100%, Jane Doe, wife
Secondary beneficiary: 100%, Jack Doe, son
Tertiary beneficiary: 100%, Jamie Doe, daughter
If Jane is living, she will receive 100%.
If Jane is deceased, Jack will receive 100%.
If Jane and Jack are deceased, Jamie will receive 100%
If all three are living at claim time, only Jane receives the beneficiary money since she was the only person named Primary.