Pet concerns surrounding head of state (6)
I believe the answer is:
caress
'pet' is the definition.
(thesaurus)
'concerns surrounding head of state' is the wordplay.
'concerns' becomes 'cares' ('care' can be a synonym of 'concern').
'surrounding' is an insertion indicator.
'head of' suggests taking the first letters.
The initial letter of 'state' is 's'.
'cares' enclosing 's' is 'CARESS'.
(Other definitions for caress that I've seen before include "Gentle stroke" , "Gentle loving touch" , "Stroke affectionately" , "Stoke affectionately" , "Embrace with affection" .)