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" describes "театре," identifying the theater as one that performs as part of a tour.
Она написала статью о гастрольном театре, который недавно посетил наш город.
She wrote an article about a traveling theater that recently visited our city.
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.