Losing face, red panda carried on, with a straight face (7)
I believe the answer is:
deadpan
'a straight face' is the definition.
(thesaurus)
'losing face' is the wordplay.
'losing' becomes 'dead' (I can't explain this - if you can you should believe this answer much more).
'face' becomes 'pan' ('pan' is old-fashioned US slang for 'face').
'dead'+'pan'='DEADPAN'
'red panda carried on with' is the link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for deadpan that I've seen before include "Showing no expression" , "With expressionless face" , "Poker-faced" , "with emotionless face" , "showing no emotion" .)