From Codebeamer 9.0.0 you can manage easily the fields of the issue list. You can add, move, remove fields, and the displaying field list is stored if you save a custom Tracker View.

To add a new field into the issue list, click one of the context menus of the header where you would like to add the field and select Add Column option. A submenu will appear where you can select which field you would like to add. The fields are grouped the same way just on the Report Page and in the Filter Widget: Default Fields, Common Reference Fields and custom fields (Project - Tracker). If a field is already in the issue list, it is grayed out and cannot be added to the current issue list.

From Codebeamer 10.1 you are able to add Shared Fields to the layout, see details here: Reports

For moving fields within the issue table, use one of the context menus Move left or Move right options or drag the label of a field and drop in another position. While dragging, a green vertical line will help you, where you can drop the field.

Additionally, you can drop the dragged field into the Filter Widget also. In this case, the field remains in its current position, but a filter / group by / order by option will be added into the Filter Widget.

For removing a field, select Remove Column option of one of the header's context menus.