Leader pushed to back of room gets through (5)

I believe the answer is:

copes

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'gets through' is the definition.
Although both the answer and definition are verbs in their -s form, I can't see how they can define each other.

I cannot understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for copes that I've seen before include "'Manages, gets by (5)'" , "Manages; church vestments" , "Somehow manages" , "Manages successfully, gets by" .)

I've seen this clue in The Guardian.

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