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The whole event was a bit more complex than a simple annexation. In XVI century Astrakhan Khanate was a point where clashed interests of Turkey and Crimean Khanate on one side, and Russia and Nogai Horde on the other, due to the importance of the city as a trading hub. The rulers changed often (basically, if a ruler leaned to one side - the other side raided the khanate and installed their marionette).
Russia only came into the picture after conquering Kazan - it came in contact with, and consequently became an ally to the Nogais. In fact, the expedition of 1554 was planned by a request from Nogay Horde ruler (well, one of the rulers - by then it was already falling to internal power struggle), and Dervish-Ali was a Nogai proponent - who actually was Astrakhanian Khan before Crimeans raided the city in 1547 and installed their own ruler. So, the goal of the expedition wasn't the conquest of the city - it was reinstallment of an allied ruler. Nogai forces failed to join the Russians for some reason, and thus Dervish-Ali became a vassal to Moscow after the victory. He almost immediately switched allegiance, though, and tried to achieve independence with Osman backing - but that, as we know, did not end well for him, and, as it was normal for Russia back then, rebel's lands were confiscated by the Tzar. After that, most of the Nogai Horde became vassals of Russian tzar, and the rest broke away and allied with Crimea and Turkey.