type
  TRichEditBeforePasteEvent = procedure(Sender: TObject; var Content: string; var CanPaste: Boolean) of object;

  TRichEdit = class(Vcl.ComCtrls.TRichEdit)
  private
    FOnAfterPaste: TNotifyEvent;
    FOnBeforePaste: TRichEditBeforePasteEvent;
    procedure CNNotify(var AMessage: TWMNotifyRE); message CN_NOTIFY;
  published
    property OnAfterPaste: TNotifyEvent read FOnAfterPaste write FOnAfterPaste;
    property OnBeforePaste: TRichEditBeforePasteEvent read FOnBeforePaste write FOnBeforePaste;
  end;

implementation

{ TRichEdit }
procedure TRichEdit.CNNotify(var AMessage: TWMNotifyRE);
var
  Content: string;
  CanPaste: Boolean;
begin
  if (AMessage.NMHdr.code = EN_PROTECTED) and (AMessage.ENProtected.msg = WM_PASTE) then
  begin
    Content := Clipboard.AsText;
    CanPaste := True;

    if Assigned(FOnBeforePaste) then
    begin
      FOnBeforePaste(Self, Content, CanPaste);
      // modify the clipboard (I don't like if someone touches what I copy there, as a
      // small workaround for that might be the try..finally block which would finally
      // restore the clipboard to the state before (and if) the OnBeforePaste modified
      // the content
      Clipboard.Clear;
      Clipboard.AsText := Content;
    end;
    // return 0 if the action is allowed; non-zero otherwise
    AMessage.Result := IfThen(CanPaste, 0, 1);

    // here I don't know how to process the "outgoing" message
    if Assigned(FOnAfterPaste) then
      FOnAfterPaste(Self);
  end
  else
    inherited;
end;

// you must set the DefAttributes.Protected to True to get the above notification
RichEdit1.DefAttributes.Protected := True;