Eating kosher in Israel can be even more complicated than in the United States. In America, there are a few kosher certifications that dominate the kosher space and it can be quite easy to find kosher products in just about any supermarket. In Israel, however, there are literally hundreds of kosher certification, making it difficult to know which ones are acceptable.
To make it simple, you really have to discuss the various certifications with your local rabbi to understand what works for you.
There are also some complications which differ between Ashkenazi and Sefardi customs.
If you want some guidance you can visit https://kosherquest.org/kosher-symbols/ for a list of acceptable certifications in Israel.