This is the 11006th most frequent Russian word.
гастрольном
"Гастрольном" refers to something related to a touring performance or tour, typically by artists or performers.
Here, "гастрольном" as an adjective describes the "tour" in which the musician is engaged, emphasizing its characteristic of being related to touring performances.
Этот музыкант успешно выступает на гастрольном туре.
This musician is successfully performing on a tour.
In this sentence, "гастрольных" modifies "мероприятий," attributing the nature of the events to be related to tours or performances conducted outside of the usual venue.
Наш офис занимается организацией гастрольных мероприятий.
Our office organizes touring events.
Here, "гастрольном" describes "театре," identifying the theater as one that performs as part of a tour.