Czech composer encountered an article in support of Suk, primarily (7)
I believe the answer is:
smetana
'czech composer' is the definition.
(I've seen this before)
'encountered an article in support of suk primarily' is the wordplay.
'encountered' becomes 'met' ('meet' can be a synonym of 'encounter').
'article' becomes 'a' (the indefinite article in English).
'in support of' is a charade indicator (letters next to each other) (in a down clue, some letters hold up others).
'primarily' indicates taking the first letters.
The first letter of 'suk' is 's'.
'met'+'an'+'a'='metana'
'metana' after 's' is 'SMETANA'.
(Other definitions for smetana that I've seen before include "Czech composer, d. 1884 - Eastman (anag)" , "maker of notes" , "musician" , "Nineteenth century Czech composer (The Bartered Bride)" , "Bedrich ____, composer of "The Bartered Bride" and "The Kiss"" .)