The most common and most likely answer to this crossword clue is the 11 letter word COUNTENANCE
I've seen this crossword clue in The Daily Telegraph
C
O
U
N
T
E
N
A
N
C
E
More clues leading to the result COUNTENANCE
Buddy explains!
The straight part
We know that "Put up with/appearance" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case put up with/appearance = countenance.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does COUNTENANCE mean?
COUNTENANCE noun- Appearance, especially the features and expression of the face.
- Favour; support; encouragement.
- Superficial appearance; show; pretense.
- Calm facial expression, composure, self-control.
- To tolerate, support, sanction, patronise or approve of something.