Waugh, say, bringing name forward, maintaining consistency (6)
I believe the answer is:
evenly
'maintaining consistency' is the definition.
(eg to paint evenly is to paint with consistency)
'waugh say bringing name' is the wordplay.
'waugh say' becomes 'even' (I can't justify this - if you can you should believe this answer much more).
'bringing' means one lot of letters go next to another.
'name' becomes 'Ly'.
'even'+'ly'='EVENLY'
'forward' acts as a link.
I am not very happy about this link. It may belong to another bit of the clue.
(Other definitions for evenly that I've seen before include "Smoothly or fairly" , "at regular intervals" , "Calmly or equitably" , "Smoothly, uniformly" , "In equal proportion" .)