Set of shelves (7)
(Other definitions for dresser that I've seen before include "Piece of furniture - theatre worker" , "behind the scenes" , "Welsh sideboard" , "Wardrobe assistant" , "Kitchen sideboard - theatre employee" .)
'set of shelves' is the definition.
(I've seen this before)
This is the entire clue.
(Other definitions for whatnot that I've seen before include "A stand with shelves for small objects" , "Thingumajig" , "Bric-a-brac stand" , "Thingummy - display stand" , "This piece of furniture" .)