PM has his own bag (9)

I believe the answer is:

gladstone

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'pm' is the definition.
(Victorian UK prime minister William Gladstone)

I don't understand the rest of the clue.

(Other definitions for gladstone that I've seen before include "Bag for a former British statesman" , "Former English PM or kind of bag" , "Old English P.M. or a doctor's bag" , "Victorian PM" , "Former British prime minister and large travelling bag" .)

I've seen this clue in The Daily Express.

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