So from what perspective are you asking this question? As a naturalized Irish citizen or as specifically former Indian citizen?
For naturalized Irish citizen there's no deadlines, hell, they can never apply for a passport at all. I know a EEA national who hasn't applied for a passport after getting his cert last year; he doesn't have an urgent need for that.
There's no travel restrictions imposed - if your IRP is still valid (or you don't need one), you're free to travel as normal.
In terms of Indian citizens, that question is better off asked in "Other countries" subforum, but looking through the embassy website, it states that
Penalty time: Penalty would be imposed if a person (including a minor) after acquisition of foreign nationality retains the Indian passport beyond three years or travels on it beyond the grace period of three months, on a passport whose final validity expired on or after 01/01/2005.
https://www.indianembassydublin.gov.in/ ... tizenship/
So formally you have three months and would assume you're naturalized when you sign the paper on the ceremony, not when certificate is delivered.
