Complex sentence: Following his brief tenure, he was succeeded by members of the Shirvanshah family who governed the city under Safavid suzerainty until 1538, after which directly appointed Safavid governors came to govern it again.
Split into simpler sentences: Following his brief tenure, he was succeeded by members of the Shirvanshah family who governed the city under Safavid suzerainty until 1538. After that, directly appointed Safavid governors came to govern it again.