No!
If you are entitled to a payment under this Agreement, this will not affect your entitlement to a payment by another State under the provisions of the EC Regulations on Social Security.
This means that you could get a payment from another State under EC Regulations and a payment from Ireland under this Agreement at the same time.
This could arise if you had been employed in Canada, Ireland and another country covered by EC Regulations.
However, when working out a person’s entitlement to a payment under this IRL/Canadian Agreement, work periods completed in the other country covered by EC Regulations will not be taken into account.
You cannot claim two Irish pensions. For example, if you qualify for one based on a combined contribution record under this Agreement with Canada and another based on a combined record with another EU State under EC Regulations, you will receive whichever Irish pension is greater.