The Midrash has many a derash on בזאת יבא אהרן as to what the word זאת refers too. One of these derashot is that it refers to Shabbat as in (ישעיה נו, ב): אַשְׁרֵי אֱנוֹשׁ יַעֲשֶׂה זֹּאת. What is the connection between Shabbat and the Kohan Gadol entering the kodesh kadashim?
The Rambam (end of Ch. 4 of Avodat Yom Hakippurim) says וְיוֹצֵא לְבֵיתוֹ וְכָל הָעָם מְלַוִּין אוֹתוֹ עַד בֵּיתוֹ וְיוֹם טוֹב הָיָה עוֹשֶׂה עַל שֶׁיָּצָא בְּשָׁלוֹם מִן הַקֹּדֶשׁ. Why does this belong in Hilchot Avodat Yom Hakippurim, what does it have to do with the avodah? The source of the Rambam is the Mishna Yoma (7:4) but the the Rambam adds the words, וְיוֹצֵא לְבֵיתוֹ, why does he add these words? The Rebbe (Likutay Sichos Acharey volume 32) explains that part of the avodah is to take it out of the kodesh kadoshim, to be able to bring the kedusha into one's life. The ויוצא מביתו is the conclusion of the avodah, to take the spiritual heights reached in the holiest place and to bring it inot one's house.
Rav Zevin explains that is the connection of Shabbat and the Kohan gadol entering the kodesh kadashim. Just as when it comes to Shabbat the point is not merely to have shabbat as a day of holiness apart from the week but to bring the kedusha of shabbat into the week, so too the Kohan Gadol must be cognizant that the kedusha that he feels in the holiest place must be able to be converted into an energy source for the year.
This is why the parsha starts with a warning from the death of Nadav and Avihu. They died בקרבתם לפני ה, they were not able to bring kedusha down and their souls expired (see Or Hachayim.) The Torah is commanding Aharon בזאת, to be able to bring the kedusha outside, not like Nadav and Avihu.
Rashi at the beginning of Kedoshim says נאמרה פרשה זו בהקהל. The Balleye Mussar say the point is that it is one thing to remain kadosh when one is in a a log cabin in the middle of nowhere but to remain a kadosh surrounded by people when one encounters with peer pressure and temptations, that is indeed a chiddush. It is when one is not in a kodesh kadoshim, that proves if one is a kadosh.