This is the 3790th most frequent Japanese word.
はせ
"はせ" can mean "to hasten" or "to rush."
In this sentence, 'はせ' is part of 'はせっかちな' (impatient), used as a description of personality.
彼女はせっかちな性格ですね。
She has an impatient personality.
Here, 'はせ' is embedded in 'はせっかく' (rare, valuable), emphasizing the importance of the missed opportunity.
旅行中に私達はせっかくのチャンスを逃した。
During the trip, we missed a rare opportunity.
In this context, 'はせ' refers to a verb form implying 'hurrying' or 'rushing', advising against it.