Appeal of centre at York (8)
I believe the answer is:
entreaty
'appeal' is the definition.
('entreaty' can be a synonym of 'appeal')
'of centre at york' is the wordplay.
'of' indicates the answer is hidden within the clue.
'ENTREATY' is hidden within 'centre at york'.
(Other definitions for entreaty that I've seen before include "suit" , "An earnest or emotional request" , "Earnest or urgent request" , "petition" , "Teeny rat (anag.)" .)