Final answer:
The mandate enacted to preclude the initial granting or renewal of security clearance eligibility by the DoD under specific circumstances is the 'Don't Ask, Don't Tell (DADT)' policy.
Step-by-step explanation:
The mandate that was enacted to preclude the initial granting or renewal of security clearance eligibility by the Department of Defense (DoD) under specific circumstances is known as Don't Ask, Don't Tell (DADT). DADT was a policy enacted by President Bill Clinton in December 1993. It allowed gay and lesbian people to serve in the military as long as they didn't come out publicly.