Part of suite, traditionally for quartet (6)
I believe the answer is:
tetrad
'quartet' is the definition.
('tetrad' can be a synonym of 'quartet')
'part of suite traditionally for' is the wordplay.
'part of' says the answer is hidden in the clue.
'TETRAD' is hidden within 'suite traditionally for'.
(Other definitions for tetrad that I've seen before include "Group or set of four" , "quartet" , "number of Gospel writers" .)