Shoot up at court before campaign (5)
I believe the answer is:
lobby
'campaign' is the definition.
(as in lobbying for a political goal)
'shoot up at court before' is the wordplay.
'shoot up at court' becomes 'lob' (as in lobbing in tennis).
'before' becomes 'by'.
'lob'+'by'='LOBBY'
(Other definitions for lobby that I've seen before include "Seek to influence (a legislator)" , "Entrance room" , "Press" , "Small hall" , "Hallway; seek to influence" .)