In order to understand what Gardiner means when he says that liberty involves a social contract and not just personal liberty, think about what he says later in the essay. Later in the essay, he says
There are a lot of people in the world, and I have to accommodate my liberty to their liberties.
What he means here is that we cannot simply think “I have liberty, and therefore I may do whatever I want.” We have to realize that there are times when our actions can take away liberty from other people.
Because our actions can take away liberty from other people, we have to have a social contract. We have to agree to give up some of our liberty in order to keep most of that liberty. Earlier in the essay, Gardiner writes about what would happen if we did not give up our liberty when told to do so by a traffic cop (or, in modern times, a stop light). If everyone tried to keep their liberty to drive whenever and wherever they wanted, no one would have any liberty to drive at all. The intersections would be jammed as everyone tried to drive at once. It would be chaos.
Therefore, we cannot simply think that liberty means that we can do whatever we want. Instead, we have to make a social contract with other people. When we do that, we all give up some of our liberties so that everyone can live together in harmony.