Starting in 425 BC, you have a guy named Cleon leading Athens. He opposed Pericles while Pericles was alive, and after his death he comes forward as the Champion of Democracy and the Voice of the People (the kind of merchant/commercial class—Cleon himself was an aristocrat). He did a lot of things differently than they’d been done in the past (to the point that Thucydides and Aristophanes represent him as a demagogue). I’ll try to provide an unbiased representation—there are positive reviews and negative reviews, so I’ll give what I can of the in-between.
Historically, Cleon is much tamer than the portrayal Aristophanes gives him (understandable because satire is larger than life/exaggerated). Aristophanes gives the character of Cleon (e.g. in Knights) a litany of comic mannerisms meant to parallel real-life Cleon. Cleon followed the tradition started by Pericles of repudiating upper-class friends made before his political career. This would become a shift in Athenian democracy, which continued at least until the ostracism of Hyperbolus around 415. Cleon, unlike Pericles, surrounded himself with an organized lower-class group, claiming that, by their guidance, his repudiation toward the right and just choices in his political life/career would be ensured (Connor).
When discussing his portrayal by Aristophanes, his associations with the lower class are pretty much a big deal. In Knights, Cleon is portrayed as a stereotypical politician (much like we still characterize some politicians today), a bottom-feeder, who can only be defeated by another politician, the Sausage Seller, who is more vulgar, louder, and brasher than the character representing Cleon. In itself, this is Aristophanes’ jab at Cleon’s aristocratic background as a wealthy manufacturer—his father owned a factory in which slaves worked hide into leather. Cleon didn’t have the “old Athenian heritage” going for him, but he was not either a member of the lower class, and Aristophanes openly makes fun of Cleon’s whole political manner.
Cleon had a distinctive oratorical style—it was a step down from the arguments of the past, which were both organized and well-presented. Cleon relied a lot on sophistry (in Aristophanes, the useful argument) as opposed to the just/righteous argument, in line with the social ideal of moral goodness. It’s a shift which began with Socrates and continued into its adoption by Cleon. Cleon also had a very interesting set of behaviors while delivering speeches and arguments (also lampooned by Aristophanes); he is noted for being the first political speaker to yell on the Pnyx to get his point across. Cleon relied more on personal charisma, it seems, than real political savvy. He was pretty effective in getting done what he wanted done, though. There was a rash of politicians after Cleon following in his footsteps, essentially, which ended with Hyperbolus, who was eventually ostracized (a process used on those who gained too much political clout).
Also, his portrayal in Thucydides was not much better than that in Aristophanes, if a little less dramatic, but for brevity’s sake I’ll leave it here.
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As Thucydides says, while he was alive, Perikles was effectively in charge of Athens. With his death, the Athenian political system could resume normal service. Before the reforms of Ephialtes and Perikles this would have meant a return to the old factional struggles between prominent leisure-class families for primacy within a nominally democratic regime watched over by a powerful council of rich elders, the Areopagos council. However, these two politicians had pushed through a number of reforms that had paved the way for Athens to become a genuine democracy. The effects of these reforms were muted by the one-man rule of Perikles; upon his death, and seemingly very suddenly, democracy came into effect.
Thucydides famously complains that Perikles was the last of the good rulers, and that after his death power fell into the hands of demagogues like Kleon, who pandered to the people and exploited the fickleness of the Assembly for their own ends. However, this is exactly what the consitution of Athens was meant to achieve. With the lowering of income barriers to office and the introduction of Assembly pay, it was now possible for a much larger section of the population to take part in politics, with the result that people who had previously not been able to challenge the primacy of old families like the Alkmaionidai (Perikles' clan) could now make themselves heard in the policy-making process. As u/euripides-eumenides notes, this shift could be a bit of a culture shock for the old elite. The new politicians didn't always play by the old rules. Kleon was known to be the first to raise his voice while on the Pnyx, and also the first to move his arms while speaking. This was not in accordance with the old ideals of dignified oratory, but it got the point across.
However, the old elite was far from gone. Some of the most prominent politicians to step into the void left by Perikles were members of the oldest, wealthiest leisure-class families. Nikias was famously rich; Alkibiades was actually another member of the Alkmaionid clan. Indeed, under the leadership of such leisure-class figures as Kritias and Theramenes, the oligarchs of Athens actually overthrew the democracy a mere 18 years after Perikles died. The project that Perikles had brought to fruition didn't fully take hold until after the restoration of democracy in 403 BC. Even then, the influence of old money remained strong, and the great families never really faded from the picture. Demagogues always had to share power to some extent with these conservative elements, and often had to yield to their superior expertise.