Rod very briefly disappearing with nasty look (4)
I believe the answer is:
leer
'nasty look' is the definition.
(I've seen this in another clue)
'rod very briefly disappearing' is the wordplay.
'rod' becomes 'lever' (I've seen this before).
'very briefly' becomes 'v' (abbreviation; 'briefly' suggests a short form).
'disappearing' suggests deleting specific letters.
'lever' with 'v' taken out is 'LEER'.
'with' acts as a link.
(Other definitions for leer that I've seen before include "Look lasciviously at" , "Look lecherously" , "unpleasant look" , "Lecherous look" , "Lascivious gaze" .)