...initially hoping its top shows are successes (4)
I believe the answer is:
hits
'are successes' is the definition.
(I've seen this in another clue)
'initially hoping its top shows' is the wordplay.
'initially' says to take the initial letters.
'its' becomes 'it' (I've seen this in other clues).
'top' says to take the initial letters (in a down clue, the first letter is top).
The initial letter of 'hoping' is 'h'.
The initial letter of 'shows' is 's'.
'h'+'it'+'s'='HITS'
(Other definitions for hits that I've seen before include "Top pops" , "In the 60s these were 'groovy'" , "welcome in the theatre world?" , "Pop successes" , "The sort of strikes" .)