'thar' is a preposition meaning 'over, beyond'. 'lear' is an older word for 'ocean, sea'. Thus 'overseas'. Given Ireland is an islands, 'overseas' and 'abroad' basically mean the same thing.
In Irish mythology, 'lear' was a personification/god of the sea. Contrary to appearances, he has nothing to do with 'King Lear'.
I said "out foreign" instead of "abroad" and honestly that's way more likely for an Irishman to say.
(I am Irish and here to improve my Gaeilge).
In the Midlands, we are much more likely to use the word "abroad" to mean "across town" or "a few towns over"
If we leave the island of Ireland we are going "out foreign"