The most common and most likely answer to this crossword clue is the 10 letter word TURNSTILES
I've seen this crossword clue in The Daily Telegraph
T
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More clues leading to the result TURNSTILES
Buddy explains!
The straight part
We know that "points of entry" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case points of entry = turnstiles.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 TURNSTILES mean?
TURNSTILES noun- A rotating mechanical device that controls and counts passage between public areas, especially one that only allows passage after a charge has been paid.
- A similar device in a footpath to allow people through one at a time while preventing the passage of cattle.
- The \vdash symbol used to represent logical entailment (deducibility relation), especially of the syntactic type; i.e., syntactic consequence. (Such symbol can be read as "prove(s)" or "give(s)". )