Unhappy that director governed while burdened (7)
I believe the answer is:
saddled
'burdened' is the definition.
('saddle' can be a synonym of 'burden')
'unhappy that director governed' is the wordplay.
'unhappy' becomes 'sad' (similar in meaning).
'that director' becomes 'd' (abbreviation eg in film reviews).
'governed' becomes 'led' (lead can mean to govern or rule).
'sad'+'d'+'led'='SADDLED'
'while' acts as a link.
This may not be correct. It may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for saddled that I've seen before include "Like a racehorse" , "Ready to ride" , "Burdened with" , "stuck" , "Encumbered" .)