Presuming it's all one itinerary, your bags should be checked all the way through meaning that all you have to do is re-clear security near your departing gate (all the outbound Ireland/U.K. flights share a secure end of the D terminal) which in my experience has also been very expedient as there is rarely a line.

You'll handle immigration and customs when you arrive in EDI as they're not part of the Schengen Agreement.