When to perform Hoshanot

Hi,

There are halachic reasons to put Hoshanot after Hallel and after Musaf. The former is sensible because the lulav is in hand and so one should complete the mitzvot performed with the lulav. The latter is sensible because the Torah reading and Musaf are actual mitzvot, which should precede the custom of Hoshanot. Our custom is to do Hoshanot after Musaf.

(Rav Moshe Feinstein, Igrot Moshe Orach Chaim 3:99)

Have a great day,
Mordechai