For the past several decades, leaders connected with Tibet at one point or another in their career were given special importance in promotion to the two highest echelons of the Communist Party of China officially known as the Politburo Standing Committee (PSC) and the Politburo.
There are plenty of examples to substantiate this claim. Former president Hu Jintao is the best example.
Hu’s connection with Tibet dated back to the late 1980s and early 1990s when he was the party secretary of the Tibet Autonomous Region and later promoted to become the standing committee member of the Politburo and eventually succeeded Jiang Zemin to become the General Secretary of the Party.[Source]