Is it possible to add a new citation after a paper is published?
No.

You cannot change a paper in any way after it is published.

The only thing you can do, is publish an erratum.  But that is intended for serious errors that affect the main conclusions, not for a "I have another related paper".

Note that many people use not only references but also citations to look for related papers.  So if the new citation is your own, newer paper, and cites your old paper, people will find the new paper from the old paper anyway if they use standard scientific databases.