Ireland Reaching Out IrelandXO is a national website for the Irish diaspora. It has an Ancestors section where people post photographs + biographical information about their ancestors. See also XO Chronicles section. Many ancestors were emigrants to North America. The website is arranged by county and then by civil parish of the ancestor if known.
https://irelandxo.comNational Museum of Ireland - Costume
https://www.museum.ie/en-IE/Collections-Research/Art-and-Industry-Collections/Art-Industry-Collections-List/CostumeNational Museums NI - Costumes and Textiles
https://www.nmni.com/collections/art/costume-and-textilesWelcome to RootsChat.
Lists of museums in Ireland, some of which have collections about clothing, textile industries, rural life, emigration.
https://en.wikipedia.org/wiki/List_of_museums_in_the_Republic_of_Irelandhttps://en.wikipedia.org/wiki/List_of_museums_in_Northern_IrelandThere are website links for some.
Bunratty Castle and Folk Park in Clare has a 19th century living village.
Dunbrody, New Ross, Wexford. Replica of a C19th sailing ship and exhibits about emigration.
Cobh heritage Centre, Cobh, cork. Life in Ireland C18th & C19th, mass emigration.
Cavan County Museum, Ballyjamesduff, Cavan - local history, culture, rural life, costumes.
They may be closed at present but there may be staff you could contact.
I've seen instructions for emigrants which included a list of clothing they should take for the voyage. It might have been for emigrants to Australia.
First impressions from the photograph. Young man was wearing a tie. Unlikely to have worn a tie for labouring or farm work. Collars were detachable and not worn when labouring. A spare shirt (if he had one), a collar and tie would be worn on Sundays and occasions when he wasn't at work, e.g. "walking out" with his sweetheart. His jacket and waistcoat were probably tweed. Missing a button on his waistcoat. Older man was wearing gaiters; suggests to me that he was an outdoors man. Were his trousers moleskin?
An important textile industry in Ireland was linen.
Where they got their clothes from depended on their income and perhaps where they lived. Long-lasting clothes such as coats might be hand-me-downs or bought second-hand. Socks and other knitted garments would be home-made. I don't know if they bought underwear or bought material to make it or cut up old shirts. May have been flannel or linen. Boots would have lasted a long time. Farmers and labourers might have lined them with something in winter to keep out the cold.
There are Irish trades directories which list businesses by county and town. Some historic editions are online. Adverts in old newspapers may be another source.
There is a photo-dating board on RootsChat. Some people who contribute to it know about clothes history. They may be able to suggest more sources of information. You could post a version of your enquiry and a link to the photo on it. Say that you have already put a question on the Ireland board.
The oldest photographs of my Irish family were taken for special occasions in early 20thC. Everyone was wearing best clothes.
A few things to bear in mind. Ireland's close connection to Britain. Frequent ships, extensive railway networks + cheap fares on both in 2nd half of 19th century. England's thriving cotton industry. Tradition of Irish people going to work in Britain on farms, in construction and factories and as hawkers and domestic servants. Some went each year for seasonal work, returning to Ireland for winter. Some remained in Britain for years. A proportion of the latter emigrated to a third country (step-migration), a proportion returned to Ireland, perhaps to take over a family farm or to care for elderly parents and a proportion settled permanently in Britain. Some of those travelling to America from Britain may have acquired clothes there, perhaps from outfitters in the departure port, if they could afford the prices. The port of Liverpool served the cotton industry in Lancashire and Cheshire. Raw cotton was imported and manufactured cotton goods were exported. A slogan was "Lancashire Cotton clothes the world". Liverpool was a major port for emigrants and for sailings to & from Ireland.
Good luck with your project.