
die Gunst
favor
Goodwill, a positive attitude, or preference that someone shows toward another person.
Durch seine Zuverlässigkeit erwarb er sich die Gunst seines Chefs.
Through his reliability, he gained the favor of his boss.
favor
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favor
Goodwill, a positive attitude, or preference that someone shows toward another person.
Durch seine Zuverlässigkeit erwarb er sich die Gunst seines Chefs.
Through his reliability, he gained the favor of his boss.

to seize the opportunity
To take advantage of a favorable opportunity or the right moment to do something.
Als alle abgelenkt waren, nutzte er die Gunst der Stunde und verließ unbemerkt die Feier.
When everyone was distracted, he seized the opportunity and left the party unnoticed.

in someone's favor
To someone's advantage or benefit.
Das Gerichtsurteil fiel zu Gunsten des Klägers aus.
The court ruling was decided in favor of the plaintiff.
'Die Gunst' (favor) belongs to the word family of 'günstig' (favorable/advantageous) and 'gönnen' (to grant someone something positive / not begrudge someone something). All of these words have the basic positive meaning of advantage or goodwill.
Das Wetter ist heute günstig für eine Wanderung.
The weather is favorable today for a hike.
The idiom 'die Gunst der Stunde nutzen' is very common. It means to seize a good opportunity immediately.
Er nutzte die Gunst der Stunde, um nach einer Gehaltserhöhung zu fragen.
He seized the opportunity to ask for a raise.
The phrase 'zu jemandes Gunsten' means 'to someone's advantage' or 'in someone's favor'. It is always formed with the genitive: 'zu meinen Gunsten' (in my favor), 'zu Gunsten des Angeklagten' (in favor of the defendant).
Die Entscheidung fiel zu Gunsten der Umwelt aus.
The decision was made in favor of the environment.
You can 'werben' (court/seek) or 'buhlen' (compete for) someone's 'Gunst' (favor). If you are successful, you 'steht man in jemandes Gunst' (are in someone's favor) or have 'erworben' (earned/acquired) their favor.
Der junge Künstler warb um die Gunst des reichen Mäzens.
The young artist sought the favor of the wealthy patron.
'Gunst' (favor) is a word of elevated style. You find it more often in historical novels, official contexts, or written language than in everyday conversation.
Der Minister verlor die Gunst des Kanzlers.
The minister lost the favor of the chancellor.
to please / to fall
„Gefallen“ describes a person or thing being appealing to someone or liked by them. „Die Gunst“, on the other hand, refers to the goodwill or preferred positive attitude one person shows toward another. Use „gefallen“ for the impression something makes and „Gunst“ for this attitude.

Der neue Bewerber genießt die Gunst der Chefin.
The new applicant enjoys the manager’s favor.
Der neue Bewerber gefällt der Chefin sehr.
The new applicant appeals to the manager a great deal.