The most common and most likely answer to this crossword clue is the 3 plus 4 letter word TWO TONE
I've seen this crossword clue in Independent
T
W
O
T
O
N
E
Buddy explains!
The straight part
We know that "like an old police siren" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case like an old police siren = two tone.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 TWO TONE mean?
TWO TONE adjective- Having two colours or shades.
- Giving two different sounds, either alternately or simultaneously.