Is it possible to declare that a Supplier needs to throw an Exception?

Edit

As pointed many times, you don’t need any custom class, use Callable and Runnable instead

Wrong, outdated solution

Consider this generic solution:

// We need to describe supplier which can throw exceptions
@FunctionalInterface
public interface ThrowingSupplier<T> {
    T get() throws Exception;
}

// Now, wrapper
private <T> T callMethod(ThrowingSupplier<T> supplier) {
    try {
        return supplier.get();
    } catch (Exception e) {
        throw new RuntimeException(e);
    }
        return null;
}

// And usage example
String methodThrowsException(String a, String b, String c) throws Exception {
    // do something
}

String result = callMethod(() -> methodThrowsException(x, y, z));