I receive an old-age pension from Israel. I have worked a few years in a country that signed a convention with Israel, and was insured there; am I allowed to claim an old-age pension from the convention country too?

​Yes. Eligibility for old-age pension in the convention country is determined and calculated according to the periods you were insured in that country. This right may not be prejudiced by the pension paid to you in Israel. 
In other words, you may receive an old-age pension from the convention country in addition to the old-age pension from Israel, subject to regular rules of entitlement.