IMPORTANT UPDATE- The port of Holyhead remains closed after Storm Darragh. There was very serious infrastructure damage caused in the storm.
Officially the port re-opens on 20 December, but most sources see this as unlikely with some saying as late as next Easter if they have to await a marine crane being brought in from the Netherlands.
The priority currently is moving freight through alternative ports, not passengers. New routes and chartered ships are being brought in for the freight traffic.
However in your situation my best advice would be to take the frequent train from Chester to Hamilton Square (Birkenhead), then walk or taxi to Birkenhead port for the Stena overnight ferry to Belfast then the train to Dublin.
This has done you a favour, as the Stena Embla and Edda are very nice ships indeed, very stylish and super steady at sea. At Belfast VT2 terminal there is a bus to Belfast Railway Station which has started from VT5 in connection with the overnight ship from Scotland. The timing is tight- I have missed it more often than I have caught it. Thus the best plan is to hop in a taxi- they will be waiting at the terminal. And one less night in a land based hotel. An efficient use of time.
If you can, and they sell out super quick, get one of the luxury balcony cabins (balcony on an 8 hour ferry ride). The upgrade is worth every penny for all the other freebies you get on that cabin grade.
EDIT 1- (17 December)- The port is now confirmed to be totally closed until AT LEAST 15 January 2025. Passengers to travel via Pembroke, Fishguard, Liverpool or Cairnryan.
EDIT 2-(18 December)- The temporary freight route from Dublin to Fishguard is now open for all passengers. It will be operated by the Stena Adventurer- departs Dublin at 22:00 and arrive in Fishguard at 05:30, a passage time of 7 hours 30 minutes. In the reverse direction, daylight sailings depart Fishguard at 09:00 and arrive to Dublin at 15:30, which is one hour less sailing time.
Local buses connect at Fishguard and there is also an 0650 train departure. That has formed an 0550 from Carmarthen (arriving 0643) so there are options.
From Stena- For passengers who were booked to travel on Holyhead – Dublin from 20th December onwards, you can transfer your booking free of charge and with no fare difference payable to alternative routes including:
Birkenhead (Liverpool) to Dublin: motorist bookings only on this route, Fishguard to Dublin, Fishguard to Rosslare, Cairnryan to Belfast, Liverpool to Belfast
Customers can amend or cancel (with full refund) their bookings online for free at stenaline.co.uk or stenaline.ie. If you prefer to speak with our team, please call us from the UK on: 00443447707070 or from ROI on: 0035319075555
Stena have said on social media that they are running a bus from Holyhead to Fishguard and return in connection with the Fishguard to Dublin sailings (need to call them for timings and booking). And Nolan Coaches in Dublin now have connecting bus services from Dublin Port to Heuston Station at 4pm from the port and 8.45pm to the port.
EDIT 3 (20 December)- Irish Ferries have today started a new daily temporary route Dublin 0930 Fishguard arrive 1500, depart 1730, Dublin arrive 2300. Open to car drivers only (No foot pax) and operated with the Isle of Innisfree, so Fishguard is becoming a busy port.