Hello, I would like to extend a Wi-Fi network, and the new extended Wi-Fi provides another ip range, with its own dhcp.
How can I do it?

Thank you

Don't do that, when changing AP the client needs to change IP, so reconnection is slowered.
By the way set wlan1 as station, add DHCP client to wlan1, create a virtual AP in ap-bridge mode and configure the new network on the Virtual AP (DHCP, gateway...) and masquerade new network.