Canvass doctor and upper class politician about university (4,2)
I believe the answer is:
drum up
'canvass' is the definition.
(as in drumming up support by canvassing votes)
'doctor and upper class politician about university' is the wordplay.
'doctor' becomes 'Dr' (abbreviation).
'and' says to put letters next to each other.
'upper class politician' becomes 'ump' (I can't explain this - if you can you should give a lot more credence to this answer).
'about' indicates putting letters inside.
'university' becomes 'u' (abbreviation for university).
'ump' placed around 'u' is 'umup'.
'dr'+'umup'='DRUM UP'
(Other definitions for drum up that I've seen before include "Bring about (something) by constant and persistent effort" , "Try to get (something) by canvassing" , "Attempt to get support by canvassing" , "Obtain through vigorous effort - and percussion?" , "To attract" .)