The action of the repressor can be summarized this way:
1. TRP repressor blocks the transcription of genes for the biosynthesis of tryptophan by the RNA polymerase.
2. TRP repressor can be active or inactive. It is active when tryptophan molecules are bound to it hence it is inactive upon the absence of tryptophan molecules. So a TRP repressor is active if the cell has tryptophan molecules in it.
3. If the TRP repressor is active, read #1.
4. If the TRP repressor is inactive, no tryptophan molecules is present in the cell thus it cannot do # 1.
5. Since the TRP repressor is inactive, the RNA polymerase will be able to transcribe the operon to produce tryptophan.
In summary, if there are enough tryptophan molecules in the cell, no transcription on the operon happening. If there are no tryptophan molecules present in the cell, the RNA polymerase will work to produce tryptophan. The activity of TRP repressor depends on the presence or absence of tryptophan.