Serious head of governing party (5)
I believe the answer is:
grave
'serious' is the definition.
('grave' can be a synonym of 'serious')
'head of governing party' is the wordplay.
'head of' suggests taking the first letters.
'party' becomes 'rave' (I've seen this before).
The first letter of 'governing' is 'g'.
'g'+'rave'='GRAVE'
(Other definitions for grave that I've seen before include "Solemn; tomb" , "Sleek, black" , "Solemn in a cemetery?" , "Serious in a crypt" , "Hazardous" .)