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

The straight part
We know that "legislative assemblies" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case legislative assemblies = senates.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 SENATES mean?
SENATES noun- In some bicameral legislative systems, the upper house or chamber.
- A group of experienced, respected, wise individuals serving as decision makers or advisors in a political system or in institutional governance, as in a university, and traditionally of advanced age and male.