Expression of ZYA is blocked. Repressor binding doesn't block RNAP binding, in fact repressor binding actually enhances RNAP binding by over 100X. This effectively traps an RNAP at the promoter. When repression is relieved by inducer, RNAP is already there and ready to go, it doesn't have to wait until an RNAP finds the promoter. The repressor protein loses affinity for the operator when it binds to an inducer . So, when lactose is present, the cell wants to use it as a carbon source.
Lactose binds the repressor and knocks it off the operator.
Then the RNAP can leave the promoter and transcribe ZYA that will cleave the lactose, bring more into the cell, and acetylate it. Once the lactose is used up, it falls off the repressor, which can bind the operator again, transcription of ZYA is shut off again.