I would strongly advise contacting the CAA directly but I think that your IAA issued cert should be good to use with the CAA PPL. The CAA will want a copy of it. When it comes to reissue, if it is being done in Ireland then ensure that the AME copies the CAA in on the issue of the new cert.
I have my class one renewed in the Mater Private each year, licence is issued by CAA and they are happy as long as the Mater forward the medical to them as well as the IAA.
rgds,
GP.