I emailed Aer Lingus HR today to find out if someone with a PPL is eligible to apply and this is the response I received.
Dear Applicant,
Many thanks for your email.
Unfortunately, the cadetship programme is only open to untrained candidates who
do not hold any licences (valid/expired)
You may apply for the Direct Entry Pilot position if advertised in the near future.
Thank you for your interest in Aer Lingus
Yours sincerely
The Aer Lingus Recruitment Team
In previous years I think it was allowed upto PPL level, so that counts me out now