Two entirely separate issues.

"Private" means that the declaration is visible only within the module.

Your 'select case' construction is a simple syntax error: you're missing the
'end select'; and in this case (as in most select case constructions) you
also need to deal with the possibility that the case will be other than
green.

Dan Kelly was telling us:
Dan Kelly nous racontait que :

If your goal is to hide the AutoNew sub form the list, you should use
ThisDocument.Document_New instead.
AutoNew and AutoOpen are deprecated.

Also, a global variable is not needed here:
For example, the following is much more reliable.
Also, your code, as is, needs to run every time the document is opened or
created for the global variable cb to equal something other than "Nothing."

Sub AutoNew()
    SetComboBox
End Sub

Private Sub SetComboBox
   Dim cb As CommandBarComboBox
    Set cb = CommandBars("Test").Controls.Add(msoControlComboBox)
    with cb
         .Caption = "ColourList"
         .OnAction = "SetColour"
         .AddItem "Green"
         ' Other setup stuff that works....
    End With
End Sub

Private Sub SetColour
    Select Case CommandBars("Test").Controls.("ColourList").Text
    Case "Green"
         'Run another Macro that doesn't matter here
EndSub