The most common and most likely answer to this crossword clue is the 7 plus 3 plus 4 letter word CATHODE RAY TUBE
I've seen this crossword clue in Financial Times
C
A
T
H
O
D
E
R
A
Y
T
U
B
E
Buddy explains!
The straight part
We know that "TV part" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case tv part = cathode ray tube.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.