Hobbes had a complex account of the relationship between passion/desire and reason. In his thinking, passion is not necessarily opposed to reason. But for the sake of simplicity, reason is concerned with long term, life goals while passion is primarily concerned with immediate goals. The ideal situation is when a person's passions correspond with their reasonable long term goals.
In other words, let's say I have enough food for one week. I might want to eat all the food I have today thus succumbing to that passion/desire, but it would benefit me to be reasonable and ration that food out for the entire week. From your quote above, this means that men (humans) are inclined to eat the food today and thereby reject saving them for the future, even though they know that the reasonable virtue is to consider the future (and even though they know there will be consequences). Man must use reason to "endeavor" (use will power) to think about the future, and about others.
When using reason, a person is more inclined to think of the big picture, long term goals, consideration of others and the state and future of community/humanity. Analogously, one needs to use reason to reconcile (combine) personal virtues such as bravery and prudence, which lead to self-preservation, with moral virtues which lead to social preservation.
In "Liberty," Hobbes talks a lot about social contracts as they relate to morality and justice and how the individual interacts with others of his/her society. The goal is a peaceful society. Individuals living in a peaceful society would necessarily be more inclined to act according to civil and moral/natural laws. When Hobbes talks about "laws of nature," he means laws which, by use of reason, correspond to eternal notions of justice and morality.
It is evident by what hath hitherto been said, how easily the laws of nature are to be observed, because they require the endeavour only, (but that must be true and constant); which whoso shall perform, we may rightly call him just.
So, men cannot divest (lose) their passions and/or selfish desires. But using reason, they can overcome them by endeavoring to behave in morally just ways which, if done with the larger picture of the peace of humanity in mind, will correspond to natural (eternal) laws of justice. Therefore in a peaceful society, civil or governmental laws, as part of the social contract between an individual and his society/government, should adhere to those natural laws of justice as well.