The Beirut bombing happened in 1983. The bombing was blamed on Islamic Jihad, but some said it was Iran and Hezbollah. Nazrallah was named to head Hezbollah 1n 1993. He could have been involved in the 1983 attack, but I don't know. He was not head of Hezbollah at the time.
New York Times says:
Mr. Nasrallah played a peripheral role in the bombing of the Marine barracks in Lebanon in 1983, killing 241 U.S. servicemen