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The people who process UK visa applications know well that there are no routine passport checks on the UK-Irish border (this arrangement is know as the Common Travel Area), so especially when the applicant resides in Ireland they would not jump to the conclusion that the earlier visa has never been used simply because there are no passport stamps to show so.
So you shouldn't need to worry in your situation.
In any case it is not a requirement for getting a visa that "previous visas must have been used". One can imagine that a large number of previous visas that appear not to have been used might make a consular officer suspicious that something might be fishy about the applicant's stated intentions -- but the most this ought to mean is that the documentation for the application is treated with particular scrutiny and suspicion.
But it seems inconceivable that one or two unused visas would have that effect. People's plans change, and consular officers know that.
(And again, an UK visa issued to a resident of Ireland would not "look unused" in the first place just because there are no stamps, because using it wouldn't produce any stamps anyway).