The most common and most likely answer to this crossword clue is the 8 letter word CHUGGERS
I've seen this crossword clue in The Guardian
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Buddy explains!
The straight part
We know that "Insistent solicitors" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case insistent solicitors = chuggers.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 CHUGGERS mean?
CHUGGERS noun- A street fundraiser, especially a private contractor, working on behalf of a charity, who is aggressive or invasive.
- One who chugs a drink, especially an alcoholic drink.
- A type of fish lure or fly that makes a popping or chugging sound when twitched.
- A vehicle or boat with an engine that makes a chugging noise when running.