I'm answering my own question after playing around with the TRESTRequest:

procedure TForm2.btnGETPOSTClick(Sender: TObject);
var
  JSONValue : TJSONValue;
  strResponse : string;
begin
  RestClient1.BaseURL := edtURL.Text;
//I found this nifty "AddAuthParameter" proc and got it working thusly
  RestRequest1.AddAuthParameter('apikey','123456789A',pkHTTPHEADER);

  RestRequest1.Execute;
  try
    strResponse := RestResponse1.Content;
    memResp.Text := strResponse;
  finally

  end;
end;