Lying urban reformer's promise may be this (9)
I believe the answer is:
crossword
'be this' is the definition.
(the crossword currently being solved is an example)
'lying urban reformer's promise' is the wordplay.
'lying urban reformer's' becomes 'cross' (I can't justify this - if you can you should give a lot more credence to this answer).
'promise' becomes 'word' (as in 'I give you my word').
'cross'+'word'='CROSSWORD'
'may' is the link.
Can you help me to learn more?
(Other definitions for crossword that I've seen before include "Letter puzzle" , "(Usually) black and white puzzle" , "Cruciverbal test" , "this, appropriately" , "See 8, 20 ac, 1, 15 dn" .)