
die Gelegenheit
opportunity
A favorable time or suitable situation to do something specific; a chance.
Nutze die Gelegenheit, um Fragen zu stellen.
Use the opportunity to ask questions.
opportunity
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opportunity
A favorable time or suitable situation to do something specific; a chance.
Nutze die Gelegenheit, um Fragen zu stellen.
Use the opportunity to ask questions.

occasion
A specific event or occasion, often of a more formal nature.
Bei dieser Gelegenheit möchte ich mich bei allen für die Unterstützung bedanken.
On this occasion, I would like to thank everyone for their support.

when there is a chance
Sometime in the future, when it works out, without naming a fixed time.
Wir können uns bei Gelegenheit mal wieder auf einen Kaffee treffen.
We can meet up for coffee again sometime when there is a chance.
'Gelegenheit' is related to the adjective 'gelegen', which means 'suitable' or 'convenient'. So a 'Gelegenheit' (opportunity) is a situation that 'gelegen kommt' (comes at a convenient time), meaning it fits well right now.
Dein Anruf kommt mir gerade sehr gelegen.
Your call is very convenient for me right now.
'Gelegenheit' is often combined with certain verbs that express how someone deals with a chance. Common collocations are 'die Gelegenheit nutzen' (to use the opportunity), 'die Gelegenheit ergreifen' (to seize the opportunity), or 'eine Gelegenheit verpassen' (to miss an opportunity).
Er hat die Gelegenheit ergriffen und sich auf die Stelle beworben.
He seized the opportunity and applied for the position.
'Gelegenheit' is very often used with an infinitive construction to describe what the opportunity is for. The pattern is: 'die Gelegenheit haben/bieten/geben, etwas zu tun' (to have/offer/give the opportunity to do something).
Auf der Konferenz hatte ich die Gelegenheit, mit vielen Experten zu sprechen.
At the conference, I had the opportunity to speak with many experts.
The expression 'bei Gelegenheit' is used to postpone a meeting or action indefinitely into the future. It signals that there is no concrete plan.
Ich rufe dich bei Gelegenheit mal an.
I'll give you a call sometime when I get the chance.
possibility
Both words can express that someone is able to do something. „Möglichkeit“ generally refers to an available option, whereas „Gelegenheit“ refers to a specific suitable situation or a favorable time to do it. When the focus is on what is possible, „Möglichkeit“ is the better fit; when the right moment arises, „Gelegenheit“ is more natural.

Nach dem Vortrag hast du die Gelegenheit, den Chef persönlich zu fragen.
After the talk, you will have the opportunity to ask the boss in person.
Du hast die Möglichkeit, den Chef per E-Mail zu fragen.
You have the option of asking the boss by email.