Once you have paid for OALD9, you should not be required to pay again to re-download it to your device or to install it on another of your devices. Firstly, please ensure that you are signed in to the App Store with the same Apple ID you used to make the purchase. Then, in the Catalogue tab of the app, tap Restore. This should allow you to access in-app purchases made with this Apple ID, i.e. to download OALD9 again at no further cost.
If you are having trouble restoring OALD8, please see here: https://oxfordeltdictionaries.zendesk.com/hc/en-us/articles/114094172252-Why-can-t-I-see-OALD8-in-the-Catalogue-tab-.
If you continue to experience difficulties, please contact us via the email link in the app.