The most common and most likely answer to this crossword clue is the 3 letter word HER
I've seen this crossword clue in Independent
H
E
R
More clues leading to the result HER
- A woman’s idol? Not altogether
- The girl’s seeing the earl regularly
- The girl’s originally employed in personnel
- That girl's pa has lost weight?
- Female parent less chubby
- The female appearing amongst others
- Daddy sheds fat for that woman
- The woman Basil cut short?
- Three Rs regularly bypassed that girl
- Woman‘s nearly arrived
Buddy explains!

The straight part
We know that "that girl" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that girl = her.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 HER mean?
HER noun- A female person or animal.
- The form of she used after a preposition or as the object of a verb; that woman, that ship, etc.