Lax and sly, keeping nothing very quiet (6)
I believe the answer is:
sloppy
'lax' is the definition.
(thesaurus)
'sly keeping nothing very quiet' is the wordplay.
'keeping' indicates putting letters inside (some letters kept inside).
'nothing' becomes 'O' (looks like zero - 0).
'very quiet' becomes 'pp' (musical abbreviation for pianissimo).
'o'+'pp'='opp'
'sly' going around 'opp' is 'SLOPPY'.
'and' is the link.
(Other definitions for sloppy that I've seen before include "Mawkish" , "Careless and messy" , "maudlin" , "'Careless, shoddy (6)'" , "Lacking neatness and order" .)