“By faith he went to live in the land of promise, as in a foreign land, living in tents with Isaac and Jacob, heirs with him of the same promise” (Heb. 11:9). Why was Abraham living in tents? Abraham lived in tents because he planned to move on. He did not plan to stay forever in the land. With a tent, you can transfer from place to place. Abraham lived in tents because he wanted to move on to another land—the city of God.
You ask, “Did he not inherit the promised land?” The answer is No. The martyr Stephen said No. Acts 7:5 reads, “Yet he gave him no inheritance in it, not even a foot’s length, but promised to give it to him as a possession and to his offspring after him, though he had no child.” God gave Abraham “no inheritance” in the promised land. It was to be his possession. But it was not to be his inheritance. Abraham knew this.
That is why in v. 9, he lived as in a foreign land, living in tents. He knew that the promised land was not to be his inheritance. Rather, the city of God is to be his inheritance. In v. 10, the writer speaks of Abraham looking forward to the city of God. “For he was looking forward to the city that has foundations, whose designer and builder is God” (Heb. 11:10). It is “the city that has foundations.” What does he mean by this? Well, a tent has no foundation. (Bengel in Ellingworth)
Near our office at IT Park, there is an ongoing project to build a building at the next block. I saw a large backhoe machine digging soil. Workers were laying large steel beams and steel rods. They were laying down a foundation before building a big building. Soon, they lay down concrete for the basement.
A tent has no foundations. But a city has foundations. You are temporary in a tent. But you are permanent in a city.
Thus, the writer may be speaking of permanence. Abraham is looking forward to living in a permanent place—the city of God, which is not on earth but in heaven.