"总理之职" can be translated into English as "the position/post of Premier" or "the role of the Premier", depending on the context.
"The position/post of Premier" emphasizes the official title or role within the government structure.
"The role of the Premier" focuses more on the functions and responsibilities associated with the position.
For example:
He assumed the position/post of Premier last year. (他去年就任总理一职。)
The role of the Premier involves overseeing the day-to-day operations of the government. (总理的职责包括监督政府的日常运作。)