When should one get his hair cut before Shavuos this year, since Erev Shavuos is Shabbos?
It is a Mitzvah to have hair cut before every Yom Tov, so as not to enter into Yom Tov unkempt. The prohibition of haircutting on Chol Hamoed was instituted especially to compel people to receive a haircut prior to Yom Tov and not to postpone it.
The necessity of receiving a haircut on erev Shavuos is more acute, because haircutting was prohibited throughout Sefirah. The long hair accumulated over Sefirah causes a disheveled appearance, which is highly inappropriate for any Yom Tov.
Minhag Chabad is to take a haircut only on Erev Shavuos (this includes the preceding night). However, since Erev Shavuos coincides with Shabbos this year, we must cut our hair one day earlier, on erev Shabbos. In his Kovetz, Rabbi Dvorkin writes: “It is obvious to me for a number of reasons that [when Erev Shavuos coincides with Shabbos,] one should receive a haircut on Erev Shabbos. In fact, I did so myself. And just as the barber began to cut my hair, his telephone rang – it was Rabbi Chodakov calling. The barber then asked me if he could go immediately to give the Rebbe a haircut…”.
There has been extensive discussion whether this includes Thursday night as well. In practice, we may be lenient about this matter.