Crossword Genius

President stable after second popper (5,4)

Ross

I believe the answer is:

press stud

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

'popper' is the definition.
(I've seen this before)

'president stable after second' is the wordplay.
I cannot quite understand how this works, but
'president' could be 'p' (common abbreviation eg in VP) and 'p' is found within the answer.
'stable' could be 'stud' (I've seen this before) and 'stud' is present in the answer.
'second' could be 're' (prefix meaning second in eg review, re-education) and 're' is found in the answer.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for press stud that I've seen before include "Virile young editor, perhaps" , "Clothes fastener" , "It may secure clothing" , "one that can hold things together" , "Popper used for fastening" .)

I've seen this clue in The Independent.
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