Branch ending rent handout (7)

I believe the answer is:

leaflet

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'handout' is the definition.
(I've seen this before)

'branch ending rent' is the wordplay.
'branch ending' becomes 'leaf' (I am not sure about this - if you are sure you should believe this answer much more).
'rent' becomes 'let' (I've seen this in another clue).
'leaf'+'let'='LEAFLET'

Can you help me to learn more?

(Other definitions for leaflet that I've seen before include "Handout sheet" , "Brochure" , "Single sheet of paper as advert" , "Handbill, flyer" , "Single printed sheet" .)

I've seen this clue in The Telegraph.

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