Initially tight on artist, match kit (9)
I believe the answer is:
trousseau
'match kit' is the definition.
(materials collected by a bride for her marriage)
'initially tight on artist' is the wordplay.
'initially tight' becomes 't' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'on' means one lot of letters go next to another.
'artist' becomes 'Rousseau' (painter Henri Rousseau, t844-t9t0).
't'+'rousseau'='TROUSSEAU'
(Other definitions for trousseau that I've seen before include "not top-drawer stuff" , "USA routes (anag.)" , "Union's present" , "Bride's clothes, linen, etc" , "Bride's outfit" .)