"For the sake of" vs "for sake of"
I don't recognise "for sake of" as an English phrase.
Looking at the iWeb corpus, I see that it does occur: 1990 instances, against 120670 of "for the sake of".
It is a much less common variant, and if I it occurred in something I was editing, I would regard it as a mistake, and add the "the".
Added to the answer by Jerzy Brzóska, 1 November 2021: It's occurrence in Google Ngrams is also at least a hundred times less common than that of "for the sake of".