Income tax liability for non resident people and no Irish income

Hello,

I'd like to understand how it works in regards to income tax liability for a person without (almost) any tie to the country. I said almost because:

- I have some pension contributions administered by a private pension fund that I am willing to keep
- some company shares waiting to mature and held by a trust (will be finishing with the transfer to my broker at the end of 2020)

I used to be a non resident landlord that sold his property last year (2019). I am in the phase of assessing taxes for 2019 and from 2020 onward I won't have any other Irish-sourced income (as I said, property sold, all accounts closed, etc.) and I won't be transferring any money to the country.

Given my situation, will I be liable for paying any taxes in 2020? How does it work with preliminary taxes I pay in 2019 on expected income in 2020 (that I won't have)?

Thank you in advance for your help!