While speaking glanced through mail, very important (3-6)
I believe the answer is:
red-letter
'very important' is the definition.
I cannot understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for red-letter that I've seen before include "Scarlet missive to signal memorable day" , "This day is memorable - hence scarlet missive" , "This day is memorable due to scarlet missive" , "(Sign of day that's) memorably important" .)