...
public slots:
    void free_pallet(QVector<int> to_free_pallet);
 
signals:
    void take_free_pallet();    //сигнал базе данных на считывание свободных мест

#include <automatic.h>
...
private:
    Automatic *automatic_wind;
 
signals:
    void send_free_pallet(QVector<int>);
 
public slots:
    void search_free_pallet();

...
    //проверка:
    emit take_free_pallet();
    qDebug()<<"signal on automatiic";
...

DataBase::DataBase(QObject *parent) : QObject(parent)
{
    qDebug()<<"it work";
 
    automatic_wind = new Automatic();
    connect(automatic_wind,&Automatic::take_free_pallet,this,&DataBase::search_free_pallet);
    connect(this,&DataBase::send_free_pallet,automatic_wind,&Automatic::free_pallet);
}
...
void DataBase::search_free_pallet(){
    qDebug()<<"search";
    QVector <int> number_pallet;
    QSqlQuery *query = nullptr;
    ...
    emit send_free_pallet(number_pallet);
    qDebug()<<"signal on database";
}