The most common and most likely answer to this crossword clue is the 6 letter word MANAGE
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More clues leading to the result MANAGE
Buddy explains!

The straight part
We know that "to cope" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case to cope = manage.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 MANAGE mean?
MANAGE noun- The act of managing or controlling something.
- (horseriding) Manège.
- To direct or be in charge of.
- To handle or control (a situation, job).
- To handle with skill, wield (a tool, weapon etc.).
- To succeed at an attempt.
- To achieve (something) without fuss, or without outside help.
- To train (a horse) in the manège; to exercise in graceful or artful action.
- To treat with care; to husband.
- To bring about; to contrive.