A question on Nazir 37a. The Gemara says
3. (Beraisa): "Mishras" forbids Ta'am k'Ikar. If one soaked grapes in water, and the water has a taste of wine, a Nazir is liable for drinking it. We learn from here to all Isurim.
4. Isurei Nazir are not permanent, they do not forbid all benefit, and there is a Heter for the Isurim. Still, the Torah forbids Ta'am k'Ikar.
My question is, how can we learn from Nazir to all Isurim? Also Chodosh has all three leniencies (Kidushin 38a). And there is a stringency to Nazir, that even Chartzanim are forbidden, which does not allow us to learn to Chatas! (Nazir 37b) Some say that the Maskana disagrees (and we can learn Chatas from Nazir), but all should agree that this is enough of a Pircha to prevent learning to Chodosh! I was tempted to say that in truth, we need to learn from a Tzad ha'Shavah of Nazir and absorptions of Chatas (37b), and we did not bring the entire Beraisa. However, it seems that the Sugya brought the entire Beraisa, for it brought the Kal va'Chomer to Kil'ayim and Orlah, even though they are not needed for the Sugya at all.
(a) Your question is asked by New Teshuvas Sha'agas Aryeh Dinei Chodosh #13.
(1) He answers according to Rashi in Kidushin 38a DH v'Yesh that Heter l'Isuro concerning Chodosh means that on 16 Nisan it is permitted when the Omer sacrifice is brought. Concerning Nazir, Rashi in Pesachim 44b DH v'Yesh writes that Heter l'Isuro means he can ask a Chacham to annul his Nezirus. According to this, Chodosh is stricter than Nazir because during the time of the prohibition of Chodosh - until 16 Nisan - there is no way that Chodosh can ever become permitted. In contrast even if someone vowed to be a Nazir for 30 days, he may undo this prohibition within the 30 days. Since Chodosh is stricter than Nazir, it is now possible to learn it from Nazir through a Kal v'Chomer with "Chad Tzad".
(2) However Tosfos in Pesachim 44b DH v'Hu writes in the name of RI that when a Nazir asks a Chacham for a Heter this is not considered Heter l'Isuro because the Chacham uproots the Nezirus right from the beginning, so this means that there was never any Nezirus. Therefore the above answer will not work according to Tosfos.
Consequently Shaagas Aryeh answers that according to RI Chodosh is not in fact learnt from Nazir through a Kal v'Chomer but rather through a Bameh Matzinu, since there is no Pircha that can be asked on the Bameh Matzinu. SA proves that one can learn with a Bameh Matzinu from the fact that the Gemara Nazir 37a wanted to learn Ta'am k'Ikar according to R. Akiva from milk and meat. There is no Kal v'Chomer here but still the Gemara was happy to learn from milk and meat (if not for the side problem that milk and meat is a Chidush).
[See SA who speaks further at length about your question]
(Incidentally one could not answer your question by trying to say that Taam k'Ikar does not in fact apply with Chodosh because see Magen Avraham 489:17 and Machtzis HaShekel that Chodosh in Eretz Yisrael makes treif utensils that it was cooked in).
[See also Sdei Chemed 3: end p. 97, #13 in the name of Yad Shaul and Teshuvas Shoel u'Meshiv 1:1:71]
(b) Your question about the stringency of Chartzanim is asked by Pirush HaRosh (below 37b). He answers that Taam k'Ikar in Kilaim and Orla is actually learnt from a combination of both Nazir and Chatas ("Osi Mibeini") through a "Bameh Hatzad".