This project is incomplete, therefore we need to continue until it is finished.

Incompletely is a rarely used adverb. So it sounds odd to my ears. I am sure the way you have used it is incorrect. But I am not sure about the way William has used it either. it would be great if someone can enlighten us on this issue. Meanwhile, You can write : * The project has not finished completely, so we have to carry it on * The project is incomplete, so we have to continue it * We have to continue the work on the project because it is incomplete * The project is not yet complete, so we have to carry on the work

This project has not finished completely, so we have to carry it on. Or This project has finished incompletely, so we have to carry it on. The 'carry on it' is wrong for the usage. Hope it helps you.