I tested the machine on many types of Trisquel's kernel-libre 10 : 5.8.0-63-generic, 5.13.0-27-generic and 5.4.0-77-generic. The wireless card, as the majority of devices, does not work with those types of Trisquel's kernel-libre due to the lack of free drivers into the kernel. Let me show you up which one of these devices don't work correctly:

According to https://seiba.gitlab.io/thinkpad-t440p-upgrade-guide/#how-to-get-around-this-wifi-whitelist, wifi technology has improved greatly over the years thanks to some clever researchers. As of 2020, the newest and currently adopted standard is 802.11ax, or Wifi 6.

The Wifi adapter found on the T440p typically only supports Wireless-N networks, or Wifi-5. And whilst this is only decent at best, you may not be taking full advantage of your network speeds.

Now how to incorperate this new technology into the T440p. You purchase a new WiFi adapter only to find out that your laptop can no longer boot properly! This is because the T440p has a Wifi whitelist.

If you want to use any other Wifi adapter, you can mod your BIOS to remove the whitelist (and also to add more functionality to your BIOS). There has been rumors that a previous BIOS may have a buggy whitelist, however this is not true.

Recently the T440p gained support for Coreboot and Libreboot. Why is this a good thing? This is a step forward into having a free and open-source BIOS firmware implementation.

Please note that if you do perform this installaton, you may find that some aspects of your device (e.g. audio) might not work as expected.

$ lspci -vmmnnk

Slot:	00:00.0
Class:	Host bridge [0600]
Vendor:	Intel Corporation [8086]
Device:	Xeon E3-1200 v3/4th Gen Core Processor DRAM Controller [0c04]
SVendor:	Lenovo [17aa]
SDevice:	ThinkPad T440p [220e]
Rev:	06
Module:	ie31200_edac


Slot:	00:02.0
Class:	VGA compatible controller [0300]
Vendor:	Intel Corporation [8086]
Device:	4th Gen Core Processor Integrated Graphics Controller [0416]
SVendor:	Lenovo [17aa]
SDevice:	ThinkPad T440p [220e]
Rev:	06
Driver:	i915
Module:	i915


Slot:	00:03.0
Class:	Audio device [0403]
Vendor:	Intel Corporation [8086]
Device:	Xeon E3-1200 v3/4th Gen Core Processor HD Audio Controller [0c0c]
SVendor:	Lenovo [17aa]
SDevice:	ThinkPad T440p [220e]
Rev:	06
Driver:	snd_hda_intel
Module:	snd_hda_intel


Slot:	00:14.0
Class:	USB controller [0c03]
Vendor:	Intel Corporation [8086]
Device:	8 Series/C220 Series Chipset Family USB xHCI [8c31]
SVendor:	Lenovo [17aa]
SDevice:	ThinkPad T440p [220e]
Rev:	04
ProgIf:	30
Driver:	xhci_hcd


Slot:	00:16.0
Class:	Communication controller [0780]
Vendor:	Intel Corporation [8086]
Device:	8 Series/C220 Series Chipset Family MEI Controller #1 [8c3a]
SVendor:	Lenovo [17aa]
SDevice:	ThinkPad T440p [220e]
Rev:	04
Driver:	mei_me
Module:	mei_me


Slot:	00:1a.0
Class:	USB controller [0c03]
Vendor:	Intel Corporation [8086]
Device:	8 Series/C220 Series Chipset Family USB EHCI #2 [8c2d]
SVendor:	Lenovo [17aa]
SDevice:	ThinkPad T440p [220e]
Rev:	04
ProgIf:	20
Driver:	ehci-pci


Slot:	00:1b.0
Class:	Audio device [0403]
Vendor:	Intel Corporation [8086]
Device:	8 Series/C220 Series Chipset High Definition Audio Controller [8c20]
SVendor:	Lenovo [17aa]
SDevice:	ThinkPad T440p [220e]
Rev:	04
Driver:	snd_hda_intel
Module:	snd_hda_intel


Slot:	00:1c.0
Class:	PCI bridge [0604]
Vendor:	Intel Corporation [8086]
Device:	8 Series/C220 Series Chipset Family PCI Express Root Port #1 [8c10]
Rev:	d4
Driver:	pcieport


Slot:	00:1c.1
Class:	PCI bridge [0604]
Vendor:	Intel Corporation [8086]
Device:	8 Series/C220 Series Chipset Family PCI Express Root Port #2 [8c12]
Rev:	d4
Driver:	pcieport


Slot:	00:1d.0
Class:	USB controller [0c03]
Vendor:	Intel Corporation [8086]
Device:	8 Series/C220 Series Chipset Family USB EHCI #1 [8c26]
SVendor:	Lenovo [17aa]
SDevice:	ThinkPad T440p [220e]
Rev:	04
ProgIf:	20
Driver:	ehci-pci


Slot:	00:1f.0
Class:	ISA bridge [0601]
Vendor:	Intel Corporation [8086]
Device:	QM87 Express LPC Controller [8c4f]
SVendor:	Lenovo [17aa]
SDevice:	ThinkPad T440p [220e]
Rev:	04
Driver:	lpc_ich
Module:	lpc_ich


Slot:	00:1f.2
Class:	SATA controller [0106]
Vendor:	Intel Corporation [8086]
Device:	8 Series/C220 Series Chipset Family 6-port SATA Controller 1 [AHCI mode] [8c03]
SVendor:	Lenovo [17aa]
SDevice:	ThinkPad T440p [220e]
Rev:	04
ProgIf:	01
Driver:	ahci
Module:	ahci


Slot:	00:1f.3
Class:	SMBus [0c05]
Vendor:	Intel Corporation [8086]
Device:	8 Series/C220 Series Chipset Family SMBus Controller [8c22]
SVendor:	Lenovo [17aa]
SDevice:	ThinkPad T440p [220e]
Rev:	04
Driver:	i801_smbus
Module:	i2c_i801


Slot:	00:19.0
Class:	Ethernet controller [0200]
Vendor:	Intel Corporation [8086]
Device:	Ethernet Connection I217-LM [153a]
SVendor:	Lenovo [17aa]
SDevice:	ThinkPad T440p [220e]
Rev:	04
Driver:	e1000e
Module:	e1000e


Slot:	03:00.0
Class:	Network controller [0280]
Vendor:	Realtek Semiconductor Co., Ltd. [10ec]
Device:	RTL8192EE PCIe Wireless Network Adapter [818b]
SVendor:	Realtek Semiconductor Co., Ltd. [10ec]
SDevice:	RTL8192EE PCIe Wireless Network Adapter [001b]
Driver:	rtl8192ee
Module:	rtl8192ee

Bus 002 Device 002: ID 8087:8000 Intel Corp. 
Bus 002 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub
Bus 001 Device 002: ID 8087:8008 Intel Corp. 
Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub
Bus 004 Device 001: ID 1d6b:0003 Linux Foundation 3.0 root hub
Bus 003 Device 003: ID 5986:0268 Acer, Inc Integrated Camera
Bus 003 Device 002: ID 1c4f:0003 SiGma Micro HID controller
Bus 003 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub

Architecture:                    x86_64
CPU op-mode(s):                  32-bit, 64-bit
Byte Order:                      Little Endian
Address sizes:                   39 bits physical, 48 bits virtual
CPU(s):                          4
On-line CPU(s) list:             0-3
Thread(s) per core:              2
Core(s) per socket:              2
Socket(s):                       1
NUMA node(s):                    1
Vendor ID:                       GenuineIntel
CPU family:                      6
Model:                           60
Model name:                      Intel(R) Core(TM) i5-4300M CPU @ 2.60GHz
Stepping:                        3
CPU MHz:                         798.161
CPU max MHz:                     3300,0000
CPU min MHz:                     800,0000
BogoMIPS:                        5187.92
Virtualization:                  VT-x
L1d cache:                       64 KiB
L1i cache:                       64 KiB
L2 cache:                        512 KiB
L3 cache:                        3 MiB