To get Promoted to the Grand Line mission you need to complete 3 key missions under the East Blue treasure log.
The 3 missions are called
"Moss-Head and Curly Brows" level 1 difficult mission
"I'm Not Letting You Get Away' level 7 difficult mission
"The Greatest Evil of the East" level 9 difficult mission
After completing "The Greatest Evil" you will also unlock Smoker as a playable character.