The most common and most likely answer to this crossword clue is the 4 plus 5 plus 3 plus 3 letter word REDS UNDER THE BED
I've seen this crossword clue in The Guardian
R
E
D
S
U
N
D
E
R
T
H
E
B
E
D
More clues leading to the result REDS UNDER THE BED
Buddy explains!
The straight part
We know that "Communists secretly" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case communists secretly = reds under the bed.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.