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喜ぶだろう

would be happy

→ 喜ぶ
phrase Rare #31,369
would be happy Expresses a prediction or supposition that someone will be pleased or happy. だろう can also mean “will probably” or “I suppose.”
JA: このプレゼントを見たら、彼女はきっと喜ぶだろう。
EN: She would surely be happy to see this present.

きっと喜ぶだろう

They’ll surely be happy.

— フィールド・オブ・ドリームス (1989)

あなたが自分で会いに行けば彼女は喜ぶだろう。

She would be happy if you went to see her yourself.

もし万が一彼女が日本に来るとすれば、ジェーンはとても喜ぶだろう。

If by any chance she were to come to Japan, Jane would be delighted.

プレゼントをあげれば、彼はもっと喜ぶだろうか。

Would he be happier if I gave him a present?

あなたにお目にかかると彼は喜ぶだろうと思います。

I think he would be pleased to meet you.