The most common and most likely answer to this crossword clue is the 9 plus 6 letter word ALEXANDRA PALACE
I've seen this crossword clue in The Times
A
L
E
X
A
N
D
R
A
P
A
L
A
C
E
Buddy explains!
The straight part
We know that "a broadcasting centre once" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a broadcasting centre once = alexandra palace.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.