Pet concerns over school head (6)
I believe the answer is:
caress
'pet' is the definition.
(thesaurus)
'concerns over school head' is the wordplay.
'concerns' becomes 'cares' ('care' can be a synonym of 'concern'**).
'over' means one lot of letters goes inside another.
'head' suggests taking the first letters.
The initial letter of 'school' is 's'.
'cares' enclosing 's' is 'CARESS'.
(Other definitions for caress that I've seen before include "Embrace with affection" , "Stroke affectionately" , "Expression of affection" , "Gentle loving touch" , "Scares into handle lovingly" .)