Prosecute university in the Home Counties (3)
I believe the answer is:
sue
'prosecute' is the definition.
(I've seen this before)
'university in the home counties' is the wordplay.
'university' becomes 'U' (abbreviation for university).
'in the' means one lot of letters goes inside another.
'home counties' becomes 'SE' (the Home Counties are in the South East of England).
'u' going within 'se' is 'SUE'.
(Other definitions for sue that I've seen before include "take to 10 [COURT] !" , "Proceed legally against (someone)" , "Start proceedings against (someone)" , "The girl to take to court" , "Take case against in court" .)