Old chairman has year in Irish county (4)
I believe the answer is:
mayo
'irish county' is the definition.
(county in Ireland)
'old chairman has year' is the wordplay.
'old chairman' becomes 'Mao' (former Chinese leader Chairman Mao).
'has' indicates putting letters inside.
'year' becomes 'y'.
'mao' placed around 'y' is 'MAYO'.
'in' acts as a link.
(Other definitions for mayo that I've seen before include "radio presenter" , "Saucy thing" , "part of Ireland" , "Irish county (county town, Castlebar)" , "Cold, creamy sauce (abbr)" .)