Some have said they would like to get rid of the DEO entirely and there's merit to that but I don't think it's as simple as having Alex quit. The DEO serves in show and production functions.
- Communications hub-This has been the DEO's primary function
- Medical bay-When Supergirl gets injured the equipment and personal to help her is available
- Science Lab
- Incarceration of superpowered villains
- This last one is a production purpose. When the stairs of the "new" DEO were designed for season two they were specifically designed to show Supergirl making dramatic entrances and exits. Those stairs have certainly served that purpose, is that a visual we want t lose. I'll also mention the balcony of deep thoughts.
Here's my solution. Have Brainy build a Supergirl communications hub out of J'onn's PI office. Bonus if a secret switch transforms the space. Taking away it's primary function will significantly reduce the DEO's presence and it happens to be the easiest to replace. There's IMO valid reasons for Alex to stay as director, Kara laid some of them out when Alex wanted to quit earlier this season. Someone should stay in a position to keep tabs on what the government is doing and ensure the alien artifacts in storage aren't misused. The only replacement I can figure out for the med bay and science lab would be L corp and that's IMO not an ideal solution. I can't think of what Supergirl could do with captured supepowered villians without being able to hand them over the the DEO.
Bottom line is I don't advocate getting rid of the DEO in season five at least. Lets move communications away and see if the sisters can function like the heads of two seperate organizations that often work together to save the planet. We'll also still have those stairs for dramatic entrances and exits. If replacements for other DEO functions can be established then it's presence can be reevaluated.