From trailer’s picked up dresser of wood (4)
I believe the answer is:
'dresser of wood' is the definition.
(tool used for dressing or shaping wood)
'from trailer's picked up' is the wordplay.
I cannot quite understand how this works, but
'from' could be 'e' (I've seen this in other clues) and 'e' is present in the answer.
'trailer' could be 'ad' (short for advert) and 'ad' is present in the answer.
A single letter 'z' remains which might be clued in a way I don't understand.
This explanation may well be incorrect...
(Other definitions for adze that I've seen before include "Woodworker's tool" , "Daze with a sort of axe" , "Something with sharp edge" , "One used to cut" , "Wood-cutting tool" .)