Will I have to re-purchase songs after resubscribing to Apple Music?

If you got the music through an Apple Music subscription, you won't be charged separately for it.

If you bought the music outside of the subscription, you won't be charged from the same country's store, but might be from a different one.

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If you are referring to "offline listening" copies of Apple Music subscription songs, you never purchased those in the first place.

Ending the original subscription will have caused them to be removed from your devices, and when you resubscribe, if you want to have "offline listening" copies of those songs again, you will need to re-download them. But there will not be any charge, over and above the cost of the subscription. The new copies will be tied to the subscription, and will stop working when it ends.

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If you are referring to songs purchased from the iTunes Store, you can usually redownload those free of charge. (In some cases, the record company or artist may have pulled a particular song and redownloading won't be an option.)

Redownload music from the iTunes Store on your iPhone or iPad - Apple Support