The most common and most likely answer to this crossword clue is the 4 letter word HERS
H
E
R
S
Buddy explains!

The straight part
We know that "it's belonging to that lady" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case it's belonging to that lady = hers.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 HERS mean?
HERS noun- A female person or animal.
- That which belongs to her; the possessive case of she, used without a following noun.