I am cutting out a section of carpet as I expand my entryway, and I want to ensure it's held down properly.

I am putting a 4' high wall up where the double red line is, and cutting out that section of carpet (later I will probably tile). Right now, there are tack strips all around except for between where I drew the two arrows. If I cut out that section, I guess I need to put new tack strips down and attach the carpet somehow. Am I going to need to use one of those carpet stretching tools to do this? Should I put tack strips down before I put the new wall in place or after? Any other suggestions about the best way to cut this and avoid problems?