In this context, "avocat constitué" refers to the attorney of record for a given party. In other words, the attorney chosen by or appointed to that party, who has filed whatever is necessary to become officially that party's representative in this case:

L'avocat constitué pour défendre le prévenu: the attorney appointed to defend the accused.

L'avocat est constitué par la famille: the lawyer is hired/engaged by the family.

There is more than one way to say, in EN, "this party's lawyer" (which is what this phrase boils down to), but "counsel of record" fits best with this particular sentence.

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Note added at 23 hrs (2020-07-28 20:38:09 GMT)
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PS: "attorney of record" works equally well. The synonym that would not work is "lawyer" -- we would pretty much never say, in a competently drafted EN legal document, "lawyer of record." It would be either "counsel of record" or "attorney of record." Perhaps in the UK they would say "barrister of record" (or "solicitor" in a non-litigation matter), but I don't know.

The lawyer (of counsel) or licensed attorney has been chosen along with his or her office's address (Mr X, Barrister); and that which is constituted (formed or made up) on the present summons and its results or consequences to follow.

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Note added at 3 days 13 hrs (2020-07-31 10:31:24 GMT)
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The source text terminology ('avocat constitue') does not mean "counsel of record". As fixed terminology it could be a 'licensed lawyer' but someone refuses to accept this. A 'licensed lawyer' would be an 'incorporated lawyer', one who is appointed to an office, dignity, designated to a function or task.
A district attorney is 'a public officer who prosecutes cases, especially criminal cases on behalf of someone or a state, usually within a defined locale or district'.
'Constituted authorities' are the officers of government, collectively, as of a city or town.
'To constitute' is to 'set up or be the elements, parts or composition of something'.
'To constitute' is 'to establish according to law or provision, a body that is duly constituted under the charter, to enact a law or regulation.'
In short, the lawyer or solicitor is one assigned to the duty implied by the case posed by the person who raised the question.

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Note added at 6 days (2020-08-02 23:57:46 GMT)
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Literally 'constitué' is 'made up of' or 'formed from'. In this legal sense the word 'licensed' refers to the lawyer's formal qualifications and recommendations. A person who is licensed holds a license which is a document that gives official, formal permission to do something.