Promote cheer around centre of Montevideo (7)
I believe the answer is:
elevate
'promote' is the definition.
('elevate' can be a synonym of 'promote')
'cheer around centre of montevideo' is the wordplay.
'cheer' becomes 'elate' (I've seen this before).
'around' means one lot of letters goes inside another.
'centre of' says to take the centre.
The middle of 'montevideo' is 'ev'.
'elate' placed around 'ev' is 'ELEVATE'.
(Other definitions for elevate that I've seen before include "Hoist" , "To raise in level" , "Raise up, hold aloft" , "Uplift" , "Lift to higher place or position" .)