A music entertainment system in Korea to dance having a cocktail (7)
I believe the answer is:
karaoke
'a music' is the definition.
(I have seen 'Japanese music ' mean 'karaoke' so perhaps 'music' could also mean 'karaoke')
'in korea to dance having a cocktail' is the wordplay.
'in' is an insertion indicator.
'to dance' indicates an anagram (letters must dance around).
'having' indicates putting letters inside.
'cocktail' becomes 'K' (the end letter or tail of the word 'cocktail').
'korea' is an anagram of 'karoe'.
'karoe' enclosing 'a' is 'karaoe'.
'karaoe' enclosing 'k' is 'KARAOKE'.
'entertainment system' acts as a link.
This may not be right. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for karaoke that I've seen before include "(Japanese) singing game" , "Amateur singing to recorded music in bars and clubs" , "Pub entertainment in which customers sing to taped music" , "Pub entertainment in which customers sing to a backing track" , "Singing along to a machine" .)