The phrase "to become secretary of state" means to be appointed or elected into the position of being in charge of a country's foreign affairs. Full definition
After becoming secretary of state at the department, her attitude to renewable energy was strongly criticised by environmentalists. (dailymail.co.uk)
There doesn't... She has failed over the course of her term — her time in office, and remember, she replaced Hillary Clinton when Hillary Clinton became Secretary of State. (maristpoll.marist.edu)
Paterson is charged with naming a replacement for Clinton, who resigned her seat to become the secretary of state in President Obama's administration. (politicalticker.blogs.cnn.com)