You would need to use the API to do this programmatically. However, you can do this by updating the CSV file before import. If you are exporting from a board layout then there will be a column field that you can change to match the appropriate column in the new project. This is only a viable alternative to using the API if it doesn’t happen that often and the exported list is fairly small. Changing a CSV file can cause other issues if you are not careful.
@Michael_Huddart, Using Advanced Search (if you’re Premium) I think this is easy to do unless I’m misunderstanding something:
Create the new (destination) project and column (if not already created)
Advanced Search > In projects > specify the source project, and then the column within the project after that is presented; also make sure to use Completion > Any
In the search results list, multi-select all tasks and change the project/column from the old to the new
I wish there was a way you could just move the column to a different project instead of having to move the tasks in the column to a new column in a different project. Trello does this and it makes management much easier. Click three dots on the top right of the column > move column > specify the board or project you want to move it to. It should be that easy.