Raise castle’s running costs (6)
I believe the answer is:
upkeep
'running costs' is the definition.
(maintenance costs)
'raise castle's' is the wordplay.
'raise' becomes 'up' (I've seen this in other clues).
'castle' becomes 'keep' (keep is a type of castle).
'up'+'keep'='UPKEEP'
(Other definitions for upkeep that I've seen before include "Cost of maintenance, say household" , "Cost of support" , "Running costs" , "Peek up at the maintenance" , "Looking after" .)