Bureaucracy involving deep art (3,4)
I believe the answer is:
red tape
'bureaucracy' is the definition.
(red tape means bureaucratic processes)
'involving deep art' is the wordplay.
'involving' indicates anagramming the letters.
'deep'+'art'='deepart'
'deepart' is an anagram of 'RED-TAPE'.
(Other definitions for red tape that I've seen before include "Unnecessary regulations" , "Irritating bureaucracy" , "legal agreement?" , "Scarlet ribbon of bureaucracy" , "Bureaucratic procedures and paperwork" .)