Effect of histidine on the binding affinity of HisP
Still if you change your question as (If histidine is abundant, HisP's job is to stop the histidine pathway as a &quot;repressor.&quot; If HisP binds less tightly to promotors, the pathway should not produce as much histidine.)
Then it should be under another assumption that what is the effect of HisP binding promoter of enzyme's gene. Is it suppressing the transcription or amplifying the transcription.
If it suppresses transcription then answer is more tightly, if it amplifies the transcription then answer is less tightly. I suggest you put this clearly in your answer, as the question is not quest accurate.

I guess your answer might be wrong.
The question should be under another assumption that how does this protein HisP regulate histidine biosynthesis. positiver or negative feedback regulation.
Generally, amino acids synthesis is regulated by negative feedback loops so that cells could control the amount of amino acids they want. In this case, the answer should be more tightly. As it functions as a repressor then it should bind promoter more tightly so that to repress the transcription more which then generate less histidine synthesis enzyme. (I believe this is what your teacher want you to answer)
In the other case, biosystems sometimes have the positive feedback regulation so that they can amplify the sensitivity to the environment noise or generate bistability (phenotypic switching). In that case, the protein bind promoter less tightly in order to generate more histidine.