Most insignificant website regularly supporting insult (9)
I believe the answer is:
slightest
'most insignificant' is the definition.
'website regularly supporting insult' is the wordplay.
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
'supporting' says to put letters next to each other (in a down clue, some letters go below others).
'insult' becomes 'slight' (I've seen this before).
The alternate letters of 'website' are 'est'.
'est' after 'slight' is 'SLIGHTEST'.
(Other definitions for slightest that I've seen before include "carrying least weight?" , "Most tenuous or meagre" , "Most tenuous or smallest" , "least important" .)