This image is from 1595, supposed to be the earliest image of a European smoking a pipe.
I read somewhere that the early Portuguese and Spanish explorers brought back tobacco and calumet pipes (not sure what those actually looked like in the 16th century, but they'd probably look kind of odd paired with a late medieval costume).
Here's Sir Walter Raleigh's pipe c. 1617:
http://tobaccopipeartistory.blogspot.com/2013/03/sir-walter-raleighs-pipe.htm
Raleigh was English, but he spent plenty of time in Ireland, so that works geographically.
Here's an odd looking pipe found at Jamestown:
http://www.cbsnews.com/news/400-year-old-tobacco-pipes-found-at-jamestown/
And here's probably what would be the more typical Elizabethan-era pipe:
http://www.historywiz.com/exhibits/james-johnrolfe.htm