The compasses will continue to point in a direction tangent to a circle centered on the wire. Don't leave the clip leads connected too long, because the electric current will rapidly drain the battery. A few seconds should be long enough to make good observations. Switch the clip leads to the other terminals of the battery. The compass needles will reverse direction when the electrical current reverses direction.
Compass needles line up with magnetic fields.
Since the earth is a magnet, a compass will normally line up with the earth's magnetic field. Because opposite magnetic poles attract, the magnetic north pole of the compass points toward the magnetic south pole of the earth. That is not a misprint. You can visualize the shape of this new field as a set of concentric circles surrounding the wire. Each of these circles has its center at the wire.