I heard once that one shouldn’t fast between Yom Kippur and the end of Sukot , not sure its reason or if it’s an accurate statement
One is allowed to fast at least on the day after Yom Kippur. See O.C. 524 that mentions a custom of some people who fast 2 consecutive days of Yom Kippur, outside of Israel because of safek hayom (uncertainty of which day is really Yom Kippur - similar to the idea applicable to other Torah holidays.) This is a custom, and it's not a common one. (I personally, know no one that does this.)
So, at least the 11th of Tishrei is permissible for fasting. I'm unaware that there are any other restrictions to fasting on any of the other days between YK and the start of Succot. Yom Tov, itself, I think has fast restrictions; I'm not sure about Hol Hamo'ed.