Correspond with a nameless politician (5)
I believe the answer is:
agree
'correspond with' is the definition.
(I've seen this before)
'a nameless politician' is the wordplay.
'nameless politician' becomes 'gree' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'a'+'gree'='AGREE'
Can you help me to learn more?
(Other definitions for agree that I've seen before include "'Assent, concur (5)'" , "'Birds in their little nest . . . . .'" , "Allow" , "grant" , "concede" .)