Gaunt head of operations keeping rogue state and America apart (10)
I believe the answer is:
cadaverous
'gaunt' is the definition.
(synonyms)
'rogue state and america apart' is the wordplay.
'rogue' becomes 'cad' (I've seen this before).
'state' becomes 'aver' (both can mean to declare).
'and' means one lot of letters go next to another.
'america apart' becomes 'ous' (I can't explain this - if you can you should give a lot more credence to this answer).
'cad'+'aver'+'ous'='CADAVEROUS'
'head of operations keeping' acts as a link.
This may not be right. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for cadaverous that I've seen before include "not looking healthy" , "Ghastly" , "Corpse-like" , "Thin and bony like a corpse" , "Unhealthy-looking" .)