The most common and most likely answer to this crossword clue is the 4 letter word CAGY
C
A
G
Y
Buddy explains!
The straight part
We know that "Not Frank!" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case not frank! = cagy.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 CAGY mean?
CAGY adjective- Wary, careful, shrewd.
- Uncommunicative; unwilling or hesitant to give information.