Crossword Genius

After payment one may let you in, at a push (9)

Ross

I believe the answer is:

turnstile

I'm a little stuck... Click here to teach me more about this clue!

'a push' is the definition.
The definition and answer can be both man-made objects as well as being singular nouns.
Maybe you can see an association between them that I can't see?

'after payment one may let you in' is the wordplay.
I cannot really understand how this works, but
'one' could be 'i' (Roman numeral) and 'i' is found within the answer.
an anagram of 'let' is 'tle' which is present in the remaining letters.
'you' could be 'u' (homophones) and 'u' is found in the answer.
This explanation may well be incorrect...

'at' is the link.

Can you help me to learn more?

(Other definitions for turnstile that I've seen before include "Admission gate" , "Rotating gate" , "gateway" , "What controls access" , "Crowd-controlling gate, at entrance to sports-ground say" .)

I've seen this clue in The Guardian.
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