Video shot covering head of state's hanging (8)
I believe the answer is:
tapestry
'hanging' is the definition.
(tapestry is a kind of hanging)
'video shot covering head of state's' is the wordplay.
'video' becomes 'tape' (I've seen this before).
'shot' becomes 'try' (I've seen this in other clues**).
'covering' is an insertion indicator.
'head of' suggests taking the first letters.
The first letter of 'state' is 's'.
'tape'+'try'='tapetry'
'tapetry' placed around 's' is 'TAPESTRY'.
(Other definitions for tapestry that I've seen before include "Embroidered wall hanging" , "Woven wall-hanging" , "Complexity" , "Fabric picture" , "Woven hanging fabric with pictures" .)