My old iPhone 6S has no service so can I move the music to my iPhone 13?

Try to get the iPhone 6S on Wi-Fi:

See the following Apple articles:

Connect to Wi-Fi on your iPhone, iPad, or iPod touch

Connect to Wi-Fi on your iPhone, iPad, or iPod touch - Apple Support

If your iPhone, iPad, or iPod touch won’t connect to a Wi-Fi network

If your iPhone or iPad won't connect to a Wi-Fi network - Apple Support

Check the route settings -> Recommended settings for Wi-Fi routers and access points

Recommended settings for Wi-Fi routers and access points - Apple Support

If you need help with your Wi‑Fi password

If you need help with your Wi‑Fi password – Apple Support (UK)

•  You need to sign in to your router.
• The Wi-Fi network name, or SSID (service set identifier), is the name your network that has a password.

If they are On, turn Off Hotspot & VPN.

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If you use the same Apple ID on your iPhone 6S and the new iPhone 13, the iTunes music would be transferred automatically.

Remove and reinsert the SIM card.

If it doesn't help visit your carrier, maybe the SIM card is damaged, ask for a replaced (new) card. Normally it is free.

Ask also to check if the SIM tray is bent, as even a tiny misalignment can cause the SIM card to not fully connect with the internal contacts in your iPhone.

See also these Apple articles below:

If you see No Service, Searching, or SOS on your iPhone or iPad

If you see No Service, Searching, or SOS on your iPhone or iPad - Apple Support

Manually update your carrier settings on your iPhone or iPad

Manually update your carrier settings on your iPhone or iPad - Apple Support

Update your network provider settings manually on your iPhone or iPad

Update your network provider settings manually on your iPhone or iPad – Apple Support (UK)

If you see a Cellular, Ultra Wideband, or Apple Pay Issue message after an iOS update or restart

If you see a Cellular, Ultra Wideband, or Apple Pay Issue message after an iOS update or restart - Apple Support