Boss losing face in dog-tired state (9)
I believe the answer is:
lassitude
'tired state' is the definition.
(state of being tired or weary)
'boss losing face in dog' is the wordplay.
'boss' becomes 'stud' (both can mean a metal decoration).
'losing face' means to remove the first letter.
'in' indicates putting letters inside.
'dog' becomes 'lassie' (I've seen this before).
'stud' with its initial letter removed is 'tud'.
'tud' placed within 'lassie' is 'LASSITUDE'.
(Other definitions for lassitude that I've seen before include "Listlessness, lethargy" , "Weariness" , "Is saluted with tiredness" , "Sluggishness" , "Listlessness, fatigue" .)