For this puzzle maybe you are:
Sitting in my star chamber, I make things prime
Arch is a hidden word in star chamber.
Synonyms for arch (as adjective) are principal, superior or premier.
I look like you, but upset
An arch in architecture looks like an inverted U
Dukes, Bishops or Angels - I am ahead of all of them
E.g. Archduke Franz Ferdinand, Archbishop of Canterbury and Archangel Gabriel
Ah, I see the end; I am very old. In short, I have the end; I keep the old
Ah - the end of ah is the end of arch
I am very old - archaic. Arch. is and abbreviation of archaic (very old)
I don't think I've got all this.
I am in a parade. I am in a ruler. I am in a hunt. I am in sugar
Parade - march, ruler - patriarch, hunt - research , sugar - starch
(Starches - complex carbohydrates - are polysaccharides or long sugar molecule chains)
Lend me your ear; I excel in quarrels
Arch can mean deliberately or affectedly playful, teasing or pointed.
Destroy me; I can burn you and start a new different puzzle
Rearrange (destroy) arch becomes char which means partially burn
And start a new puzzle - charades, a parlor game
Also hope you start a new puzzle as yours are arch meaning premier!