Not too sure what you mean there – I assume you want the shortcode to execute on the frontend so something displays for the user?
If so, have you tried this?:
<?php echo do_shortcode( '[jsoncontentimporterpro url=yes url=https://someapiwithakey123abc&iata_code=<cf_wpcf-arrival-airport\> value&type=something]' ); ?>
Then Execute PHP.
If that doesn’t work, it’s possible that the formatting of the shortcode is throwing things off. You might need to use a manual hook, instead:
add_action( 'generate_before_content', function() {
echo do_shortcode( '[jsoncontentimporterpro url=yes url=https://someapiwithakey123abc&iata_code=<cf_wpcf-arrival-airport\> value&type=something]' );
} );