Voice of host, clear, periodically rising (4)
I believe the answer is:
alto
'voice' is the definition.
(alto is a kind of voice)
'host clear periodically rising' is the wordplay.
'periodically' indicates alternate letters (letters must be selected 'every so often').
'rising' shows that the letters should be reversed in order (in a down clue, letters go up).
'host'+'clear'='hostclear'
The alternating letters of 'hostclear' are 'otla'.
'otla' reversed gives 'ALTO'.
'of' is the link.
(Other definitions for alto that I've seen before include "The highest adult male singing-voice" , "Key old > male who scores high" , "A singing voice or pitch" , "someone to sing" , "One who sings" .)