Radical at university to cede, almost subjugated (7)
I believe the answer is:
reduced
'subjugated' is the definition.
('reduce' can be a synonym of 'subjugate')
'radical at university to cede almost' is the wordplay.
'radical' becomes 'red' (I've seen this in another clue).
'at' is a charade indicator (letters next to each other).
'university' becomes 'u' (abbreviation for university).
'to' means one lot of letters go next to another.
'almost' means to remove the last letter (most of the word but not all of it).
'cede' with its last letter taken away is 'ced'.
'red'+'u'+'ced'='REDUCED'
(Other definitions for reduced that I've seen before include "Made smaller" , "Curtailed" , "Shortened" , "Abridged" , "Made less in size etc" .)