To draw or scoop up (liquid) — e.g. to pump or scoop water up from a well or container.
朝、井戸からバケツで水を汲み上げた。
In the morning I drew water from the well with a bucket.
停電のためポンプで地下水を汲み上げて給水している。
Because of the power outage they're pumping up groundwater to supply water.
急いでバケツを差し出し、泥だらけの溝から水を汲み上げた。
I hurriedly held out a bucket and scooped water up from the muddy ditch.
To draw on (ideas, opinions) — to gather and adopt input from subordinates, the public, etc.
市長は町民の声を積極的に汲み上げる姿勢を見せた。
The mayor showed a willingness to actively gather and take on the townspeople's voices.
このプロジェクトは現場の意見を汲み上げて設計が変わった。
This project changed its design after drawing on feedback from the field.
上層部が部下の考えをもっと汲み上げるべきだ。
The higher-ups should be more open to drawing on their subordinates' ideas.