Crossword Genius

What induces international to come in to face the bowling? (4)

Ross

I believe the answer is:

bait

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

'what induces international' is the definition.
I can't tell whether this defines the answer.

'come in to face the bowling?' is the wordplay.
'come in' becomes 'ait' (I am not sure about this - if you are sure you should believe this answer much more).
'to' means one lot of letters go next to another (I've seen this in other clues).
'face' suggests taking the first letters (I've seen 'face of' mean this).
The initial letter of 'bowling' is 'b'.
'ait' after 'b' is 'BAIT'.

'to' is the link.

Can you help me to learn more?

(Other definitions for bait that I've seen before include "A lure to catch fish" , "Food on a hook to attract fish" , "Annoy; enticement" , "Boilie, for example" , "Food to entice fish; taunt" .)

I've seen this clue in The Telegraph.
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