A Delhi court today ordered attachment of properties of businessman Vijay Mallya, who was declared a proclaimed offender for evading summons in a money laundering case related to FERA violation.
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The indefinite article is used to indicate one of many possible entities.
There might well be many courts in Delhi - for example a local court for the city, a provincial court, the court of appeals or the supreme court.
The sentence is telling us that one of the courts in Delhi did this.
If it was well-known that there was only one court in Delhi it would be appropriate to say "the Delhi court".
There is nothing special about government institutions. The same rules apply to "a Delhi business" or "a Delhi vagabond".
In formal official BrE, especially in legal language, there are some occasions on which the definite article would be used even though there are apparently numerous realisations of the entity described.
So, for example, it is the normal practice for English statute law to refer to "the Secretary of State" as in, for example, "Regulations made by the Secretary of State", although (in the UK but not in the USA) there are always several SofSs (SofS for Defence, SofS for Trade etc. etc.).
Similarly one will see references to "the Court" when no specific court is mentioned, and, as everybody knows, there are hundreds if not thousands of different courts.
Both usages are there partly for historical reasons (there used to be only one Secretary of State in the UK and recently, if not still, where the law requires something to be approved by "the Secretary of State" any SofS could, in legal terms, do the approving. There might be internal administrative reasons why it might be for one SofS rather than another to do so, but sometimes a signature is required immediately, so it is useful if you are not required to find just one specific person to sign.)
Similarly, the Court represented the monarch, of whom there was supposed to be only one at a time.
The other reason for using the definite article is because laws are made to last and the titles of Secretaries of State change with the whim of the Prime Minister, and even the names of courts change surprisingly frequently.
The use of the definite article in these contexts is a shorthand way of saying "whichever [SofS or court] turns out to be relevant at the time ".
In the specific case of "A Delhi court...", one suspects that these words come from a press report rather than from some official document. Depending on who the journalist thought was going to read his report that might well be a good way to convey a message without worrying the reader about which court precisely. It might not if the status of the court concerned was very high, implying that such a verdict would not be overturned, or very low (the local magistrate hearing the case when the accused was neither present nor represented) implying that the verdict was not likely to be sustained.