I discussed the assassination of Paul in some detail in an earlier response which might be of some interest. It helps to explain what happened in the aftermath of the killing. But the short version of the answer is that Alexander has been suspected of involvement or at least connivance with the plotters, and may well have had some inkling of the scheme (which was remarkably extensive and involved about 75 senior members of the Russian establishment) in advance; moreover, there's good reason to suppose that the original intention was to force Paul to abdicate, and that his killing was an unintended and regrettable consequence of the Tsar's refusal to co-operate. Alternatively, it is also possible that that, because Alexander was relatively young and lacked a strong "party" of loyalists on whom he could depend, he did not feel strong enough to move against the plotters in the aftermath of his father's death.

The reality is that Paul was a highly unpopular monarch by the time of his death, and the vast majority of those at the Russian court either supported the assassins or, at the very least, were not unhappy that the Tsar was gone. In consequence, it became clear in the immediate aftermath of the events that the murder had the support of a significant proportion of the Russian ruling class.

In addition, of course, the killing happened in the middle of the Napoleonic Wars. In these complicated circumstances, and given that the plotters represented or were actually related to a substantial swathe of Russia's governing class, Alexander very probably would not have felt able to move against them en masse even after he had established himself more securely on the throne.