The most common and most likely answer to this crossword clue is the 7 letter word ASSIZES
I've seen this crossword clue in The Guardian
A
S
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Buddy explains!

The straight part
We know that "Old courts" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case old courts = assizes.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does ASSIZES mean?
ASSIZES noun- A session or inquiry made before a court or jury.
- The verdict reached or pronouncement given by a panel of jurors.
- An assembly of knights and other substantial men, with a bailiff or justice, in a certain place and at a certain time, for public business.
- A statute or ordinance, especially one regulating weights and measures.
- Anything fixed or reduced to a certainty in point of time, number, quantity, quality, weight, measure, etc.
- Measure; dimension; size.
- A trial or hearing before such a court.