GeoTools: insert custom Polygons into existiong .shp file

I'm new to Geotools. Now I want to insert a custom area (Polygon) in a Shapefile of Austria.
My code:

 public static void main(String[] args) throws IOException {
        File file = new File("src/main/java/org/geotools/austria.shp");
        Map<String, Object> map = new HashMap<>();
        map.put("url", file.toURI().toURL());

        DataStore dataStore = DataStoreFinder.getDataStore(map);
        String typeName = dataStore.getTypeNames()[0];
        FeatureSource<SimpleFeatureType, SimpleFeature> source =
                dataStore.getFeatureSource(typeName);

        MapContent showmap = new MapContent();
        showmap.setTitle("Austria");

        Style style = SLD.createSimpleStyle(source.getSchema());
        Layer layer = new FeatureLayer(source, style);
        showmap.addLayer(layer);

        // display the map
        JMapFrame.showMap(showmap);
    }

My current result:

This image shows my current output. I drew a red hexagon to show what I want to have in future.
How can I insert and display this Polygon into a Shapefile?

First you need to create a new Shapefile (you could overwrite the old one but it is easy to lose your data that way).

SimpleFeatureType TYPE = dataStore.getSchema(typeName);
File newFile = new File("output.shp");
ShapefileDataStoreFactory dataStoreFactory = new ShapefileDataStoreFactory();

Map<String, Serializable> params = new HashMap<String, Serializable>();
params.put("url", URLs.fileToURL(newFile));
params.put("create spatial index", Boolean.TRUE);

ShapefileDataStore newDataStore = (ShapefileDataStore) dataStoreFactory.createNewDataStore(params);
newDataStore.createSchema(TYPE);

Then you need to copy the existing polygons to the new file (I'm assuming they are in a SimpleFeatureCollection called collection) followed by the new feature(s):

Transaction transaction = new DefaultTransaction("create");

String typeName = newDataStore.getTypeNames()[0];
SimpleFeatureSource featureSource = newDataStore.getFeatureSource(typeName);

if (featureSource instanceof SimpleFeatureStore) {
    SimpleFeatureStore featureStore = (SimpleFeatureStore) featureSource;

    featureStore.setTransaction(transaction);
    try {
        featureStore.addFeatures(collection);
        
        // Now add the hexagon
        featureStore.addFeatures(DataUtilities.collection(hexagon));
        transaction.commit();
     } catch (Exception problem) {
        problem.printStackTrace();
        transaction.rollback();
        System.exit(-1);
     } finally {
        transaction.close();
     }
} else {
    System.out.println(typeName + " does not support read/write access");
    System.exit(1);
}