Quote from Washington, briefly, close to Delaware (4)
I believe the answer is:
cite
'quote from' is the definition.
(I've seen this in another clue)
'washington briefly close to delaware' is the wordplay.
'washington' becomes 'city' (I've seen this in another clue).
'briefly' means to remove the last letter.
'close to' indicates one should take the final letters (the 'close' to the word).
The last letter of 'delaware' is 'e'.
'city' with its last letter removed is 'cit'.
'cit'+'e'='CITE'
(Other definitions for cite that I've seen before include "Give as an example" , "Make reference to" , "Mention as example or quote" , "Quote as authority" , "Quote as an example or in support" .)