Dirty job, head of state admitted (5)
I believe the answer is:
dusty
'dirty' is the definition.
(similar in meaning)
'job head of state admitted' is the wordplay.
'job' becomes 'duty'.
'head of' suggests taking the first letters.
'admitted' means one lot of letters goes inside another (inserted letters are admitted in).
The first letter of 'state' is 's'.
'duty' enclosing 's' is 'DUSTY'.
(Other definitions for dusty that I've seen before include "Powdery" , "Covered in fine particles" , "Dirty" , "not cleaned thoroughly" , "Study (anag.)" .)