APKUpdater Finds Updates To Your Apps Without the Google Play Store
Android: For most users, the Google Play Store is the best way to find apps and keep them updated. If you're using a non-Google ROM or downloading apps from outside the store, APKUpdater can help keep you up to date.
This app, created by XDA user rumboalla, scans your list of apps and then finds updates for those apps on sites like APKMirror. It can also optionally scrape the Google Play Store itself to find app updates. It won't automatically install the new versions, though. You'll have to download and install them one-by-one. However, it's still helpful to find out when an update is available.
This might not be necessary for most situations, but if your custom ROM doesn't have Google Play, or if you're avoiding it for privacy reasons, this is a handy way to fill in the gaps.