Since, 'school district' is being referred to one may choose an approach most appropriate for the target audience. If target audience is in US/Europe, it might be better to transliterate 'district', or even add 'school' to it (स्कूल डिस्ट्रिक्ट). Also, IMHO, using transliteration for the whole phrase (डिस्ट्रिक्ट ऑफ़ एक्सिलेंस) can also be considered, reason being it will be very intuitive for residents.
For Indian audience it must be highlighted that 'school district' is being referred to hence 'उत्कृष्ट स्कूल ज़िला' or 'उत्कृष्ट स्कूल डिस्ट्रिक्ट' would be more appropriate.
It basically comes down to the population being targeted. Also, when using in a text the sentence can be structured in a different way to make the sentence sound natural in Hindi. Please check the examples provided.