In the "Review and Conclusions" chapter of Leviathan, Hobbes makes two arguments in an attempt to persuade royalists to submit to the new government of England. After the illegal execution of Charles I by the remnants of the Long Parliament, Charles II (the "rightful" King of England) fled. The new government, called the Commonwealth, required royalists to swear an oath of loyalty by signing a document called the Engagement. Many royalists were reluctant to do so, because they still felt bound by their oaths of loyalty to Charles II.
"Besides, if a man consider that they who submit, assist the Enemy but with part of their estates, whereas they that refuse, assist him with the whole, there is no reason to call their Submission, or Composition an Assistance; but rather a Detriment to the Enemy" (Hobbes, Leviathan, from "Review and Conclusions").
In brief, Hobbes makes the following argument: Royalists who resist the Commonwealth, by refusing to swear an oath of loyalty to it, will lose all of their property (and possibly also their lives). The Commonwealth would appropriate that property, which of course would be of benefit to it. On the other hand, royalists who swear the oath of loyalty to the Commonwealth would be allowed to live and also to keep most of their property, thus preventing the Commonwealth from accruing the benefits of taking all of the royalists' land and wealth. Therefore, in order to uphold their oaths of loyalty to Charles II, royalists must swear an oath of loyalty to the Commonwealth.
This seems like a contradictory recommendation, but it actually illustrates two important aspects of Hobbes as a thinker. First, it shows his preference for pragmatic action over principled action. (This is not for me to elaborate upon here, but principled action is merely pragmatic action.) Second, it illustrates his attitude toward words and, more specifically, toward rhetoric. What matters is not the oath of loyalty someone swears, or to whom, but the intention behind the swearing of that oath (the words they speak are arbitrary to the beliefs they hold, or their true loyalty).
Hobbes was no fool, however, and he was fully aware of how this argument would be perceived by many royalists (amongst others). That is why he, in the Review and Conclusions section of Leviathan gives another argument against (violently) resisting the Commonwealth (which would have resulted in nothing more than a mass slaughter of the rebels).
"And because I find by divers English books lately printed, that the Civill warres have not yet sufficiently taught men, in what point of time it is, that a Subject becomes obliged to the Conquerour; not what is Conquest; nor how it comes about, that it obliges men to obey his Laws: Therefore for farther satisfaction of men therein, I say, the point of time, wherein a man becomes subject to a Conqueror [sic], is that point, wherein having liberty to submit to him, he consenteth, either by expresse words, or by other sufficient sign, to be his Subject" (Hobbes, Leviathan, from "Review and Conclusions").
That is, "a royalist could [swear the oath of loyalty to the Commonwealth] because a citizen's obligation to a sovereign ends when the sovereign can no longer protect him. And the exiled Charles II could not protect people in England. The fact that the Commonwealth was generated by an illegal act does not change the fact that it was now the legitimate government of England because many English subjects had joined it and it had the power to protect them" (Martinich, Hobbes, p. 16).
In short, Hobbes is telling the royalists what they can do "in good conscience," without forsaking their principles. This is a particularly shrewd appeal, because Hobbes doesn't actually believe in principles, as such, (as is illustrated by the previous argument). So Hobbes presents two reasons to forswear Charles II and swear loyalty to the new government. The first (actually the second in the text of Leviathan) appeals to the nakedly pragmatic individual; the second appeals to those who believe in the principled stance.