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Emily, your question should be written,
What is the meaning of "she is no spring chicken."

First of all, the phrase is usually written "she's no spring chicken" and it means she's not a young person. Also, the opposite expression, "she's a spring chicken," is never used.

Before artificial lighting, most hens stopped laying eggs in the winter.

The first eggs were allowed to hatch, hence "spring chickens".

A woman who is "no spring chicken" is older and tougher than she's trying to appear.