This is the 9232nd most frequent Russian word.
советской
"Советской" means "Soviet" in English, relating to the Soviet Union.
The word 'советской' is used here as an adjective in the genitive case modifying the noun 'эпохи', describing something belonging to or associated with the Soviet Union.
Это памятник советской эпохи.
This is a monument of the Soviet era.
Here, 'советской' describes the attribute of 'школы живописи' (school of painting), indicating its relation to the Soviet tradition or style.
На выставке представлены картины советской школы живописи.
The exhibition features paintings of the Soviet school of painting.
'Советской' in this instance is used to characterize the profession or origin of the writer (писательницы), tying her identity to the Soviet era or system.