We have many Mitzvot that can only be done in the Land of Israel. But how can we justify doing these Mitzvot in the southern Negev or other parts of the modern State of Israel that are not within the outlined borders of Israel in the Torah? And I heard that only once we have complete control over the biblical borders of Israel then we can extend it to newly conquered lands (I think the source is Tosfot on Gittin 8a)- but that is not currently the case. Thank you!

Rav YM Tikochinsky in his classic work Hilchot Eretz Yisrael, explains that we can not stage an offensive war to conquer areas like Eilat, before liberating all of the borders of the Promised Land, but we conquered them in a war of self defense. In this case, once the nation of Israel has an area under our rule, it receives a certain level of Kedusha, regarding certain mitzvot, e.g. there's no prohibition of leaving Eretz Yisrael to go there; there's no second day of Yom Tov there, we take off Trumot lchumra (just as a stringency)- but without a bracha, etc.