Crossword Genius

What Teddy has to look through perhaps with a hostile little pupil (5,3)

Ross

I believe the answer is:

beady eye

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

'hostile little pupil' is the definition.
I don't know anything about this answer so I can't tell whether it can be defined by this definition.

'what teddy has to look through perhaps with a' is the wordplay.
I cannot quite understand how this works, but
'look' could be 'eye' (eyeing is a kind of looking) and 'eye' is present in the answer.
'perhaps' could be 'y' (I've seen this in other clues) and 'y' is found in the answer.
'a' is present in the answer.
'teddy' could be 'ed' (I've seen this in other clues) and 'ed' is found in the leftover letters.
A single letter 'b' remains which might be clued in a way I don't understand.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for beady eye that I've seen before include "Keen (but hostile?) watchfulness" , "Attentiveness" , "viewer to be suspicious?" , "Wary observer" .)

I've seen this clue in the Irish Times (Crosaire) and the Irish Times.
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