Does the time difference between Dublin and Seoul change during the year?

Yes. Because of daylight saving time the gap moves between −9h and −8h.

When is the best time to call Seoul from Dublin?

There is no overlap between standard working days, so one side has to call early or late.

Dublin is 8h behind Seoul. This gap is not fixed: daylight saving time moves it between −9h and −8h during the year.

Dublin

Ireland

--:--:--

Seoul

South Korea

--:--:--

A 9-to-5 working day in Dublin does not overlap one in Seoul at all — somebody has to take the call outside office hours.

City	Time zone	UTC offset
Dublin · Ireland	Europe/Dublin	UTC+1
Seoul · South Korea	Asia/Seoul	UTC+9

What is the time difference between Dublin and Seoul?: Dublin is 8h behind Seoul. This gap is not fixed: daylight saving time moves it between −9h and −8h during the year.
Does the time difference between Dublin and Seoul change during the year?: Yes. Because of daylight saving time the gap moves between −9h and −8h.
When is the best time to call Seoul from Dublin?: There is no overlap between standard working days, so one side has to call early or late.