Your export is paid by your *supplier*, and you can only have one supplier for both the electricity you buy and the export you're paid for — so switching supplier moves your export arrangement to the new company. When you switch, the old supplier typically closes off your account and settles any export owed up to the switch date, often as part of the closing process (some people receive a cheque for the outstanding CEG credit a while after switching).
Practically, switching is usually manageable but can involve a lag in getting paid the final export from the old supplier, especially if they only pay export periodically (some pay every six months). The export meter reading is provided to suppliers by ESB Networks via the smart meter, so it's not generally something you enter manually. The process has been getting smoother for switchers, but it's worth being aware that the handover of export payments isn't always instant.
Because export rates differ between suppliers and contracts come and go, it's genuinely worth shopping around — both for your import tariff and your export rate — when your contract is up. A useful trick is to download your HDF data from ESB Networks and run it through a comparison tool to see which supplier's combination of import rate, standing charge and export rate actually suits your usage. Just remember that whoever you switch to becomes the one paying your export, so factor the export rate into the decision, not just the unit price.