Running battle to get given a meal round university (4)
I believe the answer is:
feud
'running battle' is the definition.
(an ongoing dispute or battle)
'given a meal round university' is the wordplay.
'given a meal' becomes 'fed' (to feed someone is to give them a meal).
'round' means one lot of letters goes inside another.
'university' becomes 'u' (abbreviation for university).
'fed' placed around 'u' is 'FEUD'.
'to get' is the link.
(Other definitions for feud that I've seen before include "Long-running quarrel" , "Persistent strife" , "Quarrel; spat" , "Long-running disagreement" , "Prolonged dispute" .)