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

The straight part
We know that "of a Greek god" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case of a greek god = priapic.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 PRIAPIC mean?
PRIAPIC adjective- Phallic.
- Related to or overly concerned with male sexual activity or exhibiting excessive male sexual activity.
- Excessively masculine; excessively concerned with masculinity.