The most common and most likely answer to this crossword clue is the 7 letter word OLYMPIA
I've seen this crossword clue in Financial Times
O
L
Y
M
P
I
A
More clues leading to the result OLYMPIA
- Cunning ploy — aim for exhibition centre
- Ignoring what’s second, just male and female spiritual games venue
- I’m struggling with old play for London venue
- Oily crooked politician entering a state capital
- In Greece, plain old folly ultimately, politician inspired by cheat no end
- A place to exhibit high heavenly home
- Old play I’m adapting in classical setting
- Not initially pious parliamentarian, one taken to a venue for godly sports
- Plain exhibition centre in the capital
- Having ejaculated, drooping, love champion returned home for games
Buddy explains!

The straight part
We know that "A place to exhibit/high heavenly home" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a place to exhibit/high heavenly home = olympia.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.