You don't say how you are doing the update.
If you use the not in list event to trigger this addition, then the event
can re-load, and re-query the combo box for you (this is built in feature).
Private Sub Distributee_NotInList(NewData As String, Response As Integer)
if MsgBox("Do you want to add this value to the list?", _
vbYesNo) then
DoCmd.OpenForm "frmAddClient", , , , acFormAdd, acDialog
Response = acDataErrAdded
Else
Response = acDataErrContinue
End If
End Sub
Note the Response = acDataErrContinue, this instructs access to reload,
and re-query the combo