County council leader’s last to be ousted (4)
I believe the answer is:
mayo
'county' is the definition.
(I've seen this before)
'council leader's last to be ousted' is the wordplay.
'council leader' becomes 'mayor'.
'last to be ousted' means to remove the last letter.
'mayor' with its last letter removed is 'MAYO'.
(Other definitions for mayo that I've seen before include "County of Western Eire" , "part of Ireland" , "You'll find it in the Emerald Isle" , "Eg, Braeburn or Cox" , "Ir. county; salad dressing" .)