Sorting a master list of names into proper 'teams'

On one sheet of my workbook (Players), I've got a master list of possible players, the eligible positions they can be used in, and the team (in our league) that has them. On another sheet (Teams), I want to be able to pull the players on each team into the headings under their team name (the teams each have a 'code' in capital letters).

When people in our league add or drop players, I want to go to the Players sheet and change the team and have those changes show up on the Teams sheet. I have other sheets that are referencing the Players sheet and that's working fine, I just can't seem to get this to work like I want it.

That's really it. I'm just tired of having to change the player names on the "Teams" sheet (effectively - since this obviously isn't the actual workbook) when I can hopefully have the file recognize the changes in a more automated way.

Thanks for the help!