Giggles start to interrupt dreadful sad song (5)
I believe the answer is:
dirge
'sad song' is the definition.
(I've seen this in another clue)
'giggles start to interrupt dreadful' is the wordplay.
'start to' says to take the initial letters.
'interrupt' indicates putting letters inside.
'dreadful' becomes 'dire' (synonyms).
The first letter of 'giggles' is 'g'.
'g' inserted within 'dire' is 'DIRGE'.
(Other definitions for dirge that I've seen before include "Funeral music" , "A slow mournful song, lament for the dead" , "Funereal hymn" , "feature of funeral" , "Threnody" .)