The most common and most likely answer to this crossword clue is the 10 letter word NIGHT-CLUB
I've seen this crossword clue in The Times
N
I
G
H
T
-
C
L
U
B
Buddy explains!
The straight part
We know that "entertainment centre" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case entertainment centre = night-club.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.