P.S. I know making a global variable is a big no-no in regards to the esthetics of the code but hopefully it can be forgiven :)

QWidget* popUpNewTime;
QTimeEdit* timeChoicePopUP;
QPushButton *button1;
void edit::on_addTime_clicked() {

    //Creating pop-up with time choice and a save button
    popUpNewTime = new QWidget(this, Qt::Popup);
    popUpNewTime->setWindowModality(Qt::WindowModal);
    QRect rect = QStyle::alignedRect(layoutDirection(), Qt::AlignBottom, QSize(width()/4, height()/6), geometry());
    popUpNewTime->setGeometry(rect);

    QVBoxLayout* layout = new QVBoxLayout(popUpNewTime);

    timeChoicePopUP = new QTimeEdit();
    button1 = new QPushButton("SAVE");

    layout->addWidget(timeChoicePopUP);
    layout->addWidget(button1);
    timeChoicePopUP->activateWindow();
    timeChoicePopUP->grabKeyboard();
    popUpNewTime->show();

    connect(button1,&QPushButton::clicked,this, &edit::addingTime);

}
void edit::addingTime() {
   timeChoicePopUP->close();
    button1->close();
    popUpNewTime->close();
}