The most common and most likely answer to this crossword clue is the 5 plus 8 letter word CAT’S WHISKERS
I've seen this crossword clue in Financial Times
C
A
T
â
€
™
S
W
H
I
S
K
E
R
S
Buddy explains!
The straight part
We know that "The best/parts of old wireless sets" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case the best/parts of old wireless sets = cat’s whiskers.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.