"Our trip is ending."
Translation:הטיול שלנו מסתיים.
Yes. But remember that since נגמר is the conjugation of both the present and the past, it can be understood as "our trip ended".
I think that נגמר means that it is already ended/finished. מסיים is in the process of ending/finishing but not yet finished.
As I wrote, נגמר is the conjugation of both past and present and it can be understood both as "is ending" or "ended". מסתיים means the same thing, in present tense. (past tense is הסתיים).