You have to differentiate between clearing for funds and clearing for fate. Clearing for funds means clearing for interest purposes, clearing for fate is in relation to potentially how long it could take for the cheque to be bounced
If you lodged this cheque in AIB on Monday(Day1), they will forward it to the other bank on the morning of day 2 and exchange value with the other bank on the same day. The other bank then has until COB on day 4 to bounce the cheque for whatever reason they like, including payment stoped, lack of funds etc.
The other bank will then send an electronic entry and the physical cheque out on the evening of day 4, these will, depending on the banks involved touch down on either Day 5 or 6, AIB would then debit your account back and that debit would normally show on Day 7. Therefore it is best to allow until Day 7 for cheques to be cleared for fate
The reason it takes so long is that antiquated banking laws require banks to send the physical paper to each other and all of the banks have centralised offices which handled this. In addition, as cheque volumes are declining, there is is no iniative for them to invest in speedier technology
Note most banks will backdate any interest to Day 1 or 2. You may be able to ask for the cheque to be cleared via special presentation, which would be faster but banks usually charge for this