The student plays their band part for you without much trouble. In rehearsal, they keep missing an entrance. Their private lesson and the director's update seem to describe different players.
Ask where it happens. Playing the notes at home doesn't necessarily include waiting through the rests, hearing the other parts, or finding the entry after a long pause.
Start before the entrance
Instead of beginning on the first note, back up into the rest. Have the student count through the measures and prepare to play at the right point. Check that they know what the meter and any markings mean.
Begin with a short wait. Then try a longer lead-in with the count still clear. If they lose track, ask where the count went missing before adding more measures.
Discuss a way to keep their place that fits the ensemble's expectations. A pencil mark at a useful landmark may help, but it needs to agree with the actual score and rehearsal instructions.
Find something else to listen for
Ask the director about a cue near the entrance. It could be another instrument's melody, a change in texture, or a clear conducting gesture.
If a suitable recording or accompaniment is available, practice with it. Count as well as listening so the student has more than one way to find the entry. A recording may use a different arrangement or tempo, so check it against the student's part.
Without a recording, you can play or sing a short surrounding line. You don't need to recreate the entire band to help them recognize a useful cue.
Rehearse getting back in
What should they do after losing their place? Look for a nearby rehearsal mark, a distinctive rhythm, or a section they can recognize. Practice finding that spot while you continue a simple accompaniment or count.
Keep the exercise short and explain the point. You're giving them a way to recover, not deliberately trying to catch them out.
Where the ensemble permits it, have them ask the director or a section partner how to rejoin if they get lost. Guessing indefinitely can make the next entrance harder to hear.
Send the director a focused question if the problem remains unclear. A little coordination between the two teachers can help you choose a lesson activity that addresses what is happening in rehearsal.