Do I need a succession order before Israeli banks will tell me what accounts my relative had?

Generally yes. Israeli banks are bound by confidentiality rules and will not disclose account information to an heir without a succession order (tzav yerusha) or a probate order (tzav kiyum tzava'a) issued by the Israeli Registrar of Inheritances or the Family Court. The Bank of Israel's dormant-accounts registry is a partial exception — it allows a basic name search without legal status — but to actually access or transfer any funds, formal legal documents are required.