Thrasymachus sustains that obedience to rulers is just (Republic, 399b7) and this comes in no contradiction with what Hobbes sustains. In a contractual society, laws must be obeyed, but this is simply the result of the renunciation of one's freedoms in return of security. However, what Hobbes always argues for in his writings is that individuals pursue their self-interest because this is their nature. Laws are restrictions in the path of pursuing one's interest. Thrasymachus makes it clear in his argumentation that he is in favour of everyone supporting their own interest and that this is the position he defends. This is one of the most obvious similarities with Hobbes. He described justice as seeking another's interest, and injustice as involving seeking one's own interest.

Hobbes supports that the ideal state of the human being is the state of nature, from which people moved to the commonwealth presented in the Leviathan. This state of nature is ideal because people are free and not constrained by any law. There is no such thing as justice or injustice in the state of nature. As individuals become part of the contractual society, they are forced to obey the laws imposed and agreed to and so they renounce their ideal freedom. With the notions of just and unjust imposed by the social contract, the individual is no longer free to pursue his own interest unless facing the consequences imposed by law. As Thrasymachus argues in his speech, those that are free and pursue their own interest are considered to be unjust.

Hobbes argues in the Leviathan that justice appears only at the creation of the commonwealth and he connects the appearance of justice with the "third law of nature," which is presented in the beginning of Chapter 15 of the Leviathan. According to...

Breaking covenants represents being unjust. Outside of a covenant, in the state of nature, individuals are free to pursue their own goal, without being obliged to respecting any law. Therefore, justice appears only when an individual agrees to be part of a contractual society.
Arguing that individuals are only free in the state of nature, where they are not forced to obey any laws, Hobbes supports the ideas presented by Thrasymachus that the idea of justice limits the liberties of individuals. However, there are some differences between Hobbes' theory of justice and what Thrasymachus understands by justice. As Thrasymachus argues, justice is made in the benefit of the ruling group. Every society has a ruling group which has the power to dictate what justice is. While Hobbes perceives justice as the third natural law according to which people are obliged to respect covenants, Thrasymachus perceives justice as being only in the advantage of the ruling class, of the stronger.

Despite the obvious similarities between the theories of the two, Hobbes does not entirely follow Thrasymachus' argumentation when claiming that only the stronger have the advantage of justice. To Hobbes, justice means respecting a covenant and respecting the agreement one has when in a contractual society, while for Thrasymachus justice is solely the advantage of the stronger.

Bibliography

Harlap, Shmuel, "Thrasymachus's justice," in Political Theory, Vol. 7, No. 3, August 1979, pp. 347-370;

Hobbes, Thomas, Leviathan, edited by Edwin Curley, Hackett Publishing Company;

Plato, the Republic, edited by G.R.F. Ferrari and translated by Tom Griffith, Cambridge University Press.