Thanks again to follower Adam Hodges-LeClaire for pointing this piece out to me.
There's a lot going on here, and for more on the political message and the various figures, I do strongly recommend reading the curators' catalog entry.
As always, I'm going to focus on the tars in this cartoon. In the frame on the left and out of frame on the right sailors bookend the piece.
This sailor wears a reversed cocked hat with a narrow brim over his bob wig. His handkerchief is worn over the jacket, but the style is indiscernible. The jacket itself is tucked into his wide legged trousers, and may be intended as a frock, as I can't make out any opening on the front. In any case, the jacket ends in slash cuffs. To emphasize his poverty, the sailor has a patch over his left knee. The trousers end about the bottom of the calf.
His uniform is decidedly that of an officer, and the trousers may be intended to make his affiliation with the sea apparent. I disagree with the curators assessment of the man standing behind him. The handkerchief over his jacket and the stick in his hand are the marks of common seamen, not officers. Neither of these objects are present on the Duke of York himself. The sailor also wears a bob wig.