Idiom for promoting someone to get rid of them
Solution 1:
"Kick Upstairs"
to promote to a nominally higher level so as to be rid of on a lower, but more effective, level, as in a corporation
Solution 2:
Perhaps the Dilbert principle (from Wikipedia):
The Dilbert principle is a concept in management developed by Scott Adams, creator of the comic strip Dilbert, which states that companies tend to systematically promote incompetent employees to management to get them out of the workflow.