Like an important day that’s embarrassed landlady? (3-6)
I believe the answer is:
red-letter
'like an important day' is the definition.
I can't tell whether this definition defines the answer.
'embarrassed landlady?' is the wordplay.
'embarrassed' becomes 'red' (someone may blush or go red when embarrassed).
'landlady?' becomes 'letter' (someone who 'lets').
'red'+'letter'='RED-LETTER'
'that's' acts as a link.
Can you help me to learn more?
(Other definitions for red-letter that I've seen before include "This day is memorable - hence scarlet missive" , "This day is memorable due to scarlet missive" , "(Sign of day that's) memorably important" , "Scarlet missive to signal memorable day" .)