It depends on the width of the fabric. If the fabric was a mile wide, it wouldn't need to be very long. If the fabric was 1 inch wide, it would have to be very long.
The arbor is 7 ft x 7 ft = 49 square feet
Whatever the width is in feet, do 49 / width and that should give you the yards needed.
If you're talking about an actual thing in the real world, you need to consider overlap. If you fill a 7 ft x 7 ft gap with a fabric that is exactly 7 ft x 7 ft, the fabric will just fall down because it isn't attached to anything.