Start to giggle about head teacher (9)
I believe the answer is:
governess
'teacher' is the definition.
(governess is a kind of teacher)
'start to giggle about head' is the wordplay.
'start to' indicates taking the first letters.
'about' becomes 'over' (I've seen this before).
'head' becomes 'ness' (ness is a headland).
The first letter of 'giggle' is 'g'.
'g'+'over'+'ness'='GOVERNESS'
(Other definitions for governess that I've seen before include "Teacher" , "Duenna" , "Mary Poppins, perhaps" , "Supernanny?" , "Becky Sharp, say" .)