Drag the clip to where you want to move it to in the Timeline. You'll see the shape of the clip move as you drag it. Align its incoming edge with the edit point you want to insert it at. So, if you have consecutive clips A, B and C and want to move clip A between clips B and C, drag clip A so that its incoming edge lines up with the incoming edge of clip C (as though you were going to overwrite clip C). Before you drop the clip, press the Option key and you'll see the arrow curve downward. This means it will insert the moved clip in its new location.
Or you could copy the clip you want to move by pressing Command+C, select it and press Shift-Delete to remove it from the current location, then move the playhead where you want the clip to go and press Shift+V, which performs an insert edit.