Singing primarily associated with someone into jazz (4)
I believe the answer is:
scat
'jazz' is the definition.
(scat is a kind of jazz)
'singing primarily associated with someone' is the wordplay.
'primarily' suggests taking the first letters.
'associated with' says to put letters next to each other.
'someone' becomes 'cat' (cat is a kind of someone**).
The first letter of 'singing' is 's'.
's'+'cat'='SCAT'
'into' acts as a link.
(Other definitions for scat that I've seen before include "improvisation in jazz" , ""Beat It"" , "unwelcome person may hear this" , "Wordless jazz singing" , "Buzz off" .)