Is Leinster pronounced “Leenster” or “Linster”? Or something else?
Something else. An Irish male here:
Seems like “Lenster” if this sample from an Irish bloke is to be believed.
ETA: Also from this pronunciation on a Youtube video of a rugby event in Leinster.
ETA 2: Damn, got ninja’d on the first cite!
It’s “Lennster” except that the title “Duke of Leinster” has its own pronunciation (of course!), which is more like “Linnster”
Thanks, all.
So, it’s the same as Leicester…makes perfect sense 
I was at the Leinster Leicester rugby cup final in 2009.
A few miles from where I live is a small town called Alcester. Many people who know about these things will be aware that the ‘ce’ in the middle is usually silent as in ‘Worcester’ pronounced Worcster so Alcester should be pronounced Alster, but it isn’t, at least not by a good many locals who will tell you that they live in Al-cest-er.