Hi
The area you describe is the overlay track and is normally relatively narrow but can appear wider if your Video track 1 has been collapsed. If you have a + sign at the far left (next to the "eye" icon) of Video track 1 then click it. This will expand the track at the expense of the overlay track. Unfortunately the overlay track (the dark band with drag and drop instructions) cannot be hidden or collapsed.
The action suggested in Borate's post works OK but at the expense of the clip preview area which is reduced in size but the video track is made wider.
However a similar enlargement can be made without affecting the preview window size and this is to grab the white bar at the top centre of the Audio track and then drag the Audio track downwards. The audio track is made narrower and the Video track wider. The preview screen remains unaltered.
Nat