если через кнопку "Sql запрос", то значение с Edit вставляется так
INSERT INTO Table2
(Day, Time, id_Specializ, Last_Name, First_Name,
Patronymic, id_Doctors, id_Price, id_Cena, Address,
Phone, id_Referal, id_Reforg, id_RefSpec, Kvit)
SELECT
Day, Time, id_Specializ, Last_Name, First_Name,
Patronymic, id_Doctors, id_Price, id_Cena, Address,
Phone, id_Referal, id_Reforg, id_RefSpec, {Edit_pacient}
FROM Table1
а так скриптом
procedure Edit_pacient_Button8_OnClick (Sender: string; var Cancel: boolean);
var
s: String;
begin
S:=Edit_pacient.Edit1.Text;
SQLExecute('INSERT INTO Temp (Day, Time, id_Specializ, Last_Name, First_Name, Patronymic, id_Doctors, id_Price, id_Cena, Address, Phone, id_Referal, id_Reforg, id_RefSpec, Kvit) SELECT Day, Time, id_Specializ, Last_Name, First_Name, Patronymic, id_Doctors, id_Price, id_Cena, Address, Phone, id_Referal, id_Reforg, id_RefSpec,kvit FROM zapicnapriem2 WHERE ZapicNaPriem2.First_Name LIKE ' +S+ ' and ZapicNaPriem2.Last_Name LIKE '+ S +' and ZapicNaPriem2.Patronymic LIKE '+S+';');
end;