It is not possible to publish unsigned APK on Google Play.
Ask from your developer for
1) source code,
2) KeyStor file[.jks file]
3) Keystore password,
4) keyAliase password
5) Generate new signed APK using keyStore file provided by your developer
6) after generating new signed APK, you can update your existing google play application by new APK.
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solved Update unsigned android apk in play store