To correct and give more information on the occasion:
If you are consecutively employed and resided in Ireland for 5 years (so after your 5th residence permit card and it's time to get 6th one) you get Stamp 4 after having Stamp 1 for 5 consecutive years. I arrived and registered in Ireland in June 2016, my work permit started on May 2016. At June 2021, I got stamp 4 based on working and living in Ireland consecutively for 5 years.
There is nothing like you can get work permit only for 60 months or 5 years. You can get work permit how long you want. I got work permit for 7 years and on my 6th year of my work permit I switched to Stamp 4. And the durations of my work permits were 2 years + 3 years (same employer) and then I asked my new employer to get me 2 years of work permit, but I didn't need to use last year of it.
And to fix your statement
The problem is that, in order to apply for the stamp 4, one needs to have 60 months of reconable residence which is counted from the moment when one comes to Ireland and applies and receives the card (not from the dates on employment permit or work visa).
You have to be working consecutively every year after you are in Ireland, so if you come to Ireland in 2022, you need to be employed at 2022, 2023, 2024, 2025, 2026 and only then you can get Stamp 4 on 2027.
If you are on Stamp 1 = you need work permit. If you somehow switch to Stamp 4 by, getting married with Irish or Eu citizen, or obtaining critical skills etc etc then you won't be in need of work permit. If you have on going work permit when you get stamp 4, then it won't cause any problem, as you won't need it anymore.
I didn't get the citizenship part of your question so have no comment about it.