Jackass periodically brought up Jamaican music (3)
I believe the answer is:
ska
'jamaican music' is the definition.
(Jamaican music genre)
'jackass periodically brought up' is the wordplay.
'periodically' means one should take alternating letters (letters must be selected 'every so often').
'brought up' shows that the letters should be reversed in order (in a down clue, letters go up).
The alternate letters of 'jackass' are 'aks'.
'aks' written backwards gives 'SKA'.
(Other definitions for ska that I've seen before include "Noted genre" , "Jamaican music, forerunner of reggae" , "Music genre" , "popular music" , "Dancehall music" .)