Install second network interface on virtualized Ubuntu Server

I've solved the problem adding

# The secondary network interface
auto enp0s8
iface enp0s8 inet dhcp

to /etc/network/interfaces

(Get the new interface name using ifconfig -a)

and restarting the network using sudo service networking restart.

Now, here is the result of

$ ifconfig enp0s3    Link encap:Ethernet  HWaddr 08:00:27:47:52:7b  
          inet addr:192.168.56.101  Bcast:192.168.56.255  Mask:255.255.255.0
          inet6 addr: fe80::a00:27ff:fe47:527b/64 Scope:Link
          UP BROADCAST RUNNING MULTICAST  MTU:1500  Metric:1
          RX packets:6334 errors:0 dropped:0 overruns:0 frame:0
          TX packets:7656 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:1000 
          RX bytes:2741526 (2.7 MB)  TX bytes:10824219 (10.8 MB)

enp0s8    Link encap:Ethernet  HWaddr 08:00:27:3e:1e:bf  
          inet addr:10.0.3.15  Bcast:10.0.3.255  Mask:255.255.255.0
          inet6 addr: fe80::a00:27ff:fe3e:1ebf/64 Scope:Link
          UP BROADCAST RUNNING MULTICAST  MTU:1500  Metric:1
          RX packets:8 errors:0 dropped:0 overruns:0 frame:0
          TX packets:16 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:1000 
          RX bytes:1730 (1.7 KB)  TX bytes:1882 (1.8 KB)

lo        Link encap:Local Loopback  
          inet addr:127.0.0.1  Mask:255.0.0.0
          inet6 addr: ::1/128 Scope:Host
          UP LOOPBACK RUNNING  MTU:65536  Metric:1
          RX packets:2143 errors:0 dropped:0 overruns:0 frame:0
          TX packets:2143 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:1 
          RX bytes:443165 (443.1 KB)  TX bytes:443165 (443.1 KB)

if it's on an updated Ubuntu server that doesn't use ifup, enter your new config into the /etc/netplan/50-cloud-init.yaml instead:

network:
  ethernets:
     enp0s3:
        dhcp4: true
     enp0s8:
        dhcp4: true
version: 2

and then run:

netplan apply

then it should pop up!