The most common and most likely answer to this crossword clue is the 7 letter word GRECIAN
I've seen this crossword clue in The Times
G
R
E
C
I
A
N
More clues leading to the result GRECIAN
- Style of architecture old lady found around Clerkenwell area?
- Classically simple part of City toured by old lady
- Attic in which old lady hides gems from the east
- Nana smuggling crystal meth back from Athens?
- Grace in unusual style of classical architecture
- Attic needs clearing out after student leaves
- Germanic cast wanting male from Athens?
- Classical grace in dancing
- Misplaced nice rag from a Mediterranean land
- One from southern Europe racing round with hidden energy
Buddy explains!

The straight part
We know that "Classically simple" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case classically simple = grecian.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.