Spiteful university’s pursuing college (amongst seven) (7)
I believe the answer is:
vicious
'spiteful' is the definition.
(I've seen this before)
'university's pursuing college amongst seven' is the wordplay.
'university's' becomes 'ou's'.
'pursuing' means one lot of letters go next to another.
'college' becomes 'c'.
'amongst' indicates putting letters inside (I've seen this in other clues).
'seven' becomes 'VII' (roman numeral).
'c' inserted into 'vii' is 'vici'.
'ous' put after 'vici' is 'VICIOUS'.
(Other definitions for vicious that I've seen before include "Strongly spiteful and dangerous" , "Deliberately cruel or violent" , "Malicious, brutal" , "Malicious - degenerate" , "Deliberately nasty" .)