You can find research positions for postdoc at several universities in Israel. students can continue their research under the supervision of experienced researchers, the research is usually conducted in English.
Admittance is usually decided according to PhD achievements. Fellowship requests must be submitted within 3 years of finishing one's doctoral studies.
There are several universities in Israel that conduct research in sciences such as chemistry and genetic engineering. My advice to you is to contact the universities in order to make sure they employ researchers in your field. You can try universities such as the Technion in Haifa, Weizmann Institute in Rehovot or Bar Ilan University in Ramat Gan.
You can also read more about the programs in the link below my answer.