| Nazir
When one thinks of the mitzvoth dependent on the land of Israel we think of the agricultural laws of the Torah; terumah, maaser, shmittaand the like. One surely does not think of the nazir, a law that seemingly applies both in Israel and out and has no connection to the land. Yet think of nazir we must. 
"One who vowed a series of nezeeroots and completed them and afterwards comes to the land [of Israel] Beit Shammai says must be a nazir for thirty days and Beit Hillel says he is a nazir as he vowed before[1]" (Nazir 19b). While these two great schools of learning debate whether a token nezeeroot of 30 days is sufficient or whether one must match the length of nezeeroot observed outside the land, all agree that the nezeeroot must be redone in Israel. What is left unexplained is why? There seems little to connect nezeeroot and the land of Israel. 
The Torah teaches that "all the days of nezeeroot he (or she) is holy to G-d" (Bamidbar 6:7). It is for this reason that, with the exception of a meit mitzva, an unattended body, a nazir may not come in contact with death. Kedusha and death are mutually exclusive [2]. We attain holiness by the way we conduct our lives; death brings impurity. It is for this reason a kohen who also has an elevated status of kedusha, holinessmay not come in contact with death. The kedusha of the kohen is most manifest in his role of Torah teacher - "for the priest's lips should keep knowledge, and they should seek the law at his mouth; for he is the messenger of the Lord of hosts" (Malachai 2:7)- it is a life of Torah that embodies kedusha. Holiness itself is most manifest - and perhaps can only be achieved - in the Land of Israel. It is where we are closer to the Divine from whence holiness emanates[3]. It is thus impossible to completely fulfill the imperative to be holy outside of Israel. Our Sages went so far as to declare impurity to the Diaspora lands, tumat eretz haamim.
Thus one who takes a vow of nezeeroot outside of Israel must - at least on a Rabbinic level[4] - fulfill that vow in the land of Israel even if they had already done so outside of Israel.
This is powerfully illustrated by the case of Queen Helena, queen of Adiabe, a country in Asia Minor,and a 1st century convert to Judaism, whose "son went to war and she said 'if my son comes from the war in peace I will be a nazirite for seven years', and her son came back from the war and she was a nazirite for seven years. At the end of seven years she went up to the land of Israel and Beit Hillel ruled that she should be a nazirite for seven more years" (Nazir 19b). 

But the story does not end here. "At the end of seven years she became impure [by contact with the dead], so we find that she was a nazirite for twenty-one years".  When a nazir becomes impure they must start their nezeeroot over again - and over again means in this instance seven more years. Even if we accept the view of Rav Yehuda who claims that Helena followed the less stringent view of Rabbi Eliezer that one who becomes tameh need only observe a thirty day period of nezeroot 14 years and 30 days is a long time.

[1]This Mishna appears twice in the Talmud once here and once in masechet Eduyot, testimonies, where the Mishna lists 39 cases - out of 316 disputes - where Beit Hillel is stringent and Beit Shammai take the lenient approach.
 
[2] At times Jews are called upon to give up their life "to sanctify the Name". the sanctification is in choosing to do so not in death itself. Beyond these limited cases one is forbidden to give up one's life even if it means violating mitzvoth of the Torah. A person for whom fasting is dangerous is obligated to eat on Yom Kippur.
  
[3] The same can be said regarding simcha, joy. Complete joy is achieved when felling the presence of G-d something only fully done in Israel. Thus the mitzva to rejoice on your festival requires one celebrate at the Temple, the central resting place of the Divine presence. Even the Askenazic custom for kohanim to duchen - to combine the holy and the joyous - in the Diaspora only on Yom tov stems from the notion that joy is only fully experienced in Israel. As only those filled with joy can bless others the practice developed to limit duchenim to the joyous times of the festivals. 
  
[4] The commentaries debate as to whether the nezeeroot in Israel is a rabbinic stringency to be observed if and when one moves to Israel or whether one who takes a vow to become a nazir must in fact immediatedy move to Israel (Rambam, Nazir 2:21).