The most common and most likely answer to this crossword clue is the 7 letter word CZARINA
I've seen this crossword clue in Independent
C
Z
A
R
I
N
A
More clues leading to the result CZARINA
Buddy explains!

The straight part
We know that "Important lady" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case important lady = czarina.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does CZARINA mean?
CZARINA noun- An empress of several Eastern European countries, especially Russia, or the wife of a tsar.