Learn Turkish: Hangi sefer gecikmek üzere? - Which trip is about to be delayed?

When üzere follows a verb in its full infinitive form (ending in -mAk or -mEk), it means "about to" or "on the verge of". So, gecikmek üzere translates to "about to be delayed".

Does sefer refer to a specific type of trip, like a flight?

Sefer is a broad word for any scheduled journey, run, or voyage. Depending on where you are, it could mean "flight" (at an airport), "ferry crossing" (at a dock), or "bus trip" (at a terminal). It can also just mean "time" or "instance", as in bu sefer (this time).

Where is the word for "is" in this sentence?

It is implied at the end of the sentence. In the third person ("it is"), the "to be" suffix -dir is often dropped in spoken Turkish. In a formal announcement, you might hear this as gecikmek üzeredir, but leaving it off is very common and grammatically correct.

I've learned that -mAk üzere can sometimes mean "in order to". Could I swap it with için here?

No, that would change the meaning entirely! While -mAk üzere can sometimes mean "in order to" (similar to için), when it is used at the end of a sentence like this, it almost always means "is about to". If you said gecikmek için, the sentence would mean "in order to be delayed."