This is the 6903rd most frequent Russian word.
актерское
Relating to acting or an actor.
The word "актерское" is used here as an adjective to describe "мастерство" — in this case, indicating the quality related to the profession of acting.
Его актёрское мастерство оставило всех зрителей под впечатлением.
His acting skills left all the viewers impressed.
"Актерское" is applied here to "искусство" to specify the form of art that pertains to acting.
Анна решила развивать своё актёрское искусство и записалась на курсы.
Anna decided to develop her acting art and enrolled in courses.
Here, "актерское" modifies "талантом", referring to the talent one exhibits in the field of acting or theatrical performances.