Our Gemara on Amud Beis strongly implies that there is no mitzvah of Aliyyah Leregel (Yom Tov Pilgrimage) in our times where there is no Bais HaMikdash:

תִּינַח בִּזְמַן שֶׁבֵּית הַמִּקְדָּשׁ קַיָּים בִּזְמַן שֶׁאֵין בֵּית הַמִּקְדָּשׁ קַיָּים מַאי אִיכָּא לְמֵימַר 

The Gemara raises a difficulty: This works out well when the Temple is standing, as there are those who ascend to Jerusalem for the pilgrimage Festival at that time. However, when the Temple is not standing what can be said? 

It is a matter of dispute amongst acharonim whether indeed there is a mitzvah in our times to do aliyyah leregel, with different places in Shas giving different indications. For example, see שדי חמד ח"ו, פאת השדה מערכת א"י ט וספר חסידים תר״ל. I would like to focus on a fascinating Teshuva of the Noda BeYehuda (II:OC:94) where he takes the position that there is no mitzvah of Aliyya Leregel in today’s times but then goes further to assert that this exempts a person from the commandment to “greet their master on the holiday“ מקביל פני רבו ברגל. 

The sages (Rosh Hashanah 16b) teach us that there is a special commandment to meet their rebbe on the festivals:

וְאָמַר רַבִּי יִצְחָק: חַיָּיב אָדָם לְהַקְבִּיל פְּנֵי רַבּוֹ בָּרֶגֶל, שֶׁנֶּאֱמַר: ״מַדּוּעַ אַתְּ הוֹלֶכֶת אֵלָיו הַיּוֹם לֹא חֹדֶשׁ וְלֹא שַׁבָּת״, מִכְּלָל דִּבְחֹדֶשׁ וְשַׁבָּת אִיבְּעִי לַהּ לְמֵיזַל.

The Gemara cites two more statements in the name of Rabbi Yitzḥak, relating to the Festivals: And Rabbi Yitzḥak said: A person is obligated to go out and greet his teacher on a Festival, as it is stated that the husband of the Shunamite woman asked, when she was readying herself to go to the prophet: “Why will you go to him today; it is neither the New Moon nor Shabbos” (II Kings 4:23). 

The proof text that the Gemara uses is puzzling and questioned by many commentaries. The verse seems to imply that there is an obligation, or at least customary expectation, to greet their Rebbe on Shabbos and Rosh Chodesh. And, somehow, from this, we say that one is obligated to greet their Rebbe on the festivals. If we are going to use this proof text, should that not mean an application for every Shabbos and every Rosh Chodesh, aside from the festival?

The Noda BeYehuda’s resolution to this is as follows: In truth, because we bring a Mussaf Sacrifice on Shabbos and Rosh Chodesh and there is a resulting greater holiness of the day one, should be obligated to greet his Rebbe every Shabbos and Rosh Chodesh. However, because of another teaching, which we shall soon see, one cannot give more honor to his master than to God. And, since (for practical reason most likely), the Torah only obligated a pilgrimage three times a year for the festivals, then the obligation can be no greater than that to meet his master. This explains why, even though the Gemara records this as an obligation, we do not find it codified in Tur and Shulkhan Arukh.

אֵין תַּלְמִיד חָכָם רַשַּׁאי לַעֲמוֹד מִפְּנֵי רַבּוֹ אֶלָּא שַׁחֲרִית וְעַרְבִית כְּדֵי שֶׁלֹּא יִהְיֶה כְּבוֹדוֹ מְרוּבֶּה מִכְּבוֹד שָׁמַיִם 

A Torah scholar is permitted to stand before his teacher only once in the morning and once in the evening, so that the teacher’s honor should not be greater than the honor of Heaven, as one recites the Shema, which is tantamount to greeting God, once in the morning and once in the evening.  (Kiddushin 33b)

Because one cannot give more honor to his Rebbe, then to God, since nowadays, we no longer obligated to make a pilgrimage on the festival, Noda BeYehuda reasons this is why we also are no longer obligated to greet one’s rebbe on the festival that is why it is not codified.

There are some other novel answers to the question as to why the proof text can come from Rosh Chodesh and Shabbos, and yet the obligation to greet the Rebbe only applies on festivals. One of the most interesting and creative answers that I have seen comes from the Peri Tzaddik (Parashas Hachodesh). When the husband said to the Shunamite woman, “Today is not a new moon, today is not a Shabbos, why are you going to greet the prophet?” he was referring to the idea that when there is a new awareness of holiness on shabbos or Rosh Chodesh and that is the time to meet one’s Torah teacher. However, asserts Rav Tzaddok, the typical person cannot reach such a holy state without it being a COMBINATION of festival and Shabbos. After all, he reasons, every festival has a shabbos within it because they last an entire week. (Even Shavuous, while only one day, allows for a full week of bringing festival sacrifices.). And, when one reaches that double state of holiness, then a spiritual encounter is incumbent upon him. The husband of the Shunamite woman, who was aware of their higher, spiritual potential, understood that they might be obligated to greet their rebbe every Shabbos and Rosh Chodesh. But for the regular folk, the understanding was only a combination of festival and Shabbos, or possibly Rosh Chodesh and Shabbos. And that is how the obligation was recorded.

I will conclude with an observation about what is the function of greeting one's master on the festival in particular. One might think that when one is at the highest spiritual state, he or she might need less connection to the teacher. But apparently that is not the Torah approach. To the contrary, when one is in an ecstatic spiritual state this is precisely when one needs feedback and grounding from their tradition so it does not lead to antinomianism.