The news of a new terminal at the Sky Harbor airport was kind of out of the blue. It seems the proposed new terminal will be in the old Terminal 2 location; so it won't impact Tempe directly. More details are expected on May 7th.
The news
https://www.abc15.com/news/region-ph...harbor-airport pointed me to the 2019 pdf
https://www.skyharbor.com/media/k4eh...2019-09-13.pdf (see page 32) that talks about the proposed West Terminal under the heading "Preferred Terminal Concept".
While a new terminal on the west side may not have a direct impact on Tempe skyline, but more flights, especially more international flights, would have an indirect impact on Tempe.