I have Spartan Airways on Hoover and I just opened a new subsidiary in UK (my legal country is France). After I set the flights (LTN - TLV / LTN - IST) I saw that no PAX booked on my flights which is almost zero problable and I want to ask you if I opened a new subsidiary in UK do I have the right to transport PAX from UK to non EU countries?
No. Legal country = Flight rights from that country only. So in this case, you can serve destinations outside the EU only when the flight starts from France.
Thanks for the answer. That means I create that new subsidiary in vane? I will never be able to set flights to outside EU starting outside France?
Correct. You can fly from UK to Italy, Greece, Sweden and so on… But not outside European union. If you want to fly longer than EU, it can only be from France.
But if I will open an subsidiary in Israel or Egypt for example, do I have traffic rights? I understood that I don't have traffic rights inside the EU if I already have the legal country in one of EU's country, but is this applying to all countries?
It applies to all countries. Your holding is generally (see note) is limited to one set of traffic rights, based on your legal country. So in your case France. If that legal country is a signatory to an open skies agreement you are entitled to those as per the agreement.
Note: It is possible to get another set of traffic rights if you open a subsidiary in an open investment country, or a more complex model via the stock market
Short answer: if you open a sub in Egypt or Isreal the only tickets you can sell if between France and Egypt or Isreal