I would like to ask the difference between the sentences below.
1. Please do inform your supervisor for a consent.
2. Please inform your supervisor for a consent.
g. to reinforce a statement or to contradict an opposite statement. There seems no particular reason to use it in your example.
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This "do" adds emphasis, e.g. to reinforce a statement or to contradict an opposite statement. There seems no particular reason to use it in your example. However, the question is rendered somewhat irrelevant by the fact that the sentence as a whole does not make sense. It could be that this is meant:
Please ask your supervisor for permission.
You don't 'inform someone for a consent'. You ask/request someone for his/her consent.
We usually say sentence #2.
Sentence #1 is only used in a context where you are insisting.
eg
Tom: Please ask your supervisor for her consent.
Jim: No, I won't.
Tom: It's important. Please do ask her for her consent.