It doesn't follow that disheartened syndicate should leave old city after French refusal (3,8)
I believe the answer is:
non sequitur
'it doesn't follow' is the definition.
(I've seen this in another clue)
'disheartened syndicate should leave old city after french refusal' is the wordplay.
'disheartened' suggests removing the centre (the middle or heart is removed).
'should leave' becomes 'quit' (I can't justify this - if you can you should believe this answer much more).
'old city' becomes 'ur' (ancient city state).
'after' is a charade indicator (letters next to each other).
'french refusal' becomes 'non' ('no' in French).
'syndicate' with its middle removed is 'se'.
'se'+'quit'+'ur'='sequitur'
'sequitur' after 'non' is 'NON-SEQUITUR'.
'that' acts as a link.
Can you help me to learn more?
(Other definitions for non sequitur that I've seen before include "one doesn't follow on" , "Statement not expected" , "Reply that has no relevance to what was said before" , "Irrelevant reply" , "Illogical conclusion" .)