The most common and most likely answer to this crossword clue is the 7 letter word WIRETAP
I've seen this crossword clue in The Sunday Telegraph
W
I
R
E
T
A
P
Buddy explains!

The straight part
We know that "Secretly listen to" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case secretly listen to = wiretap.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 WIRETAP mean?
WIRETAP noun- A connection installed on a telephone line or other communications system in order to allow a third party to conduct covert surveillance of conversations.
- To install or to use such a connection.