You could set a different Linux-libre kernel version in your operating system declaration, e.g. (kernel (@ (gnu packages linux) linux-libre-5.10)) or (kernel (@ (gnu packages linux) linux-libre-5.4)).
If you don’t mind recompiling your kernel: Searching in my /run/current-system/kernel/.config reveals a few occurrences of HDMI in the kernel configuration. You could set in your operating system declaration: (kernel ((@@ (gnu packages linux) make-linux-libre*) (@@ (gnu packages linux) linux-libre-5.14-version) (@@ (gnu packages linux) linux-libre-5.14-gnu-revision) (@@ (gnu packages linux) linux-libre-5.14-source) '("x86_64-linux") #:configuration-file (@@ (gnu packages linux) kernel-config) #:extra-options (append '(("CONFIG_SND_HDA_INTEL" . #f)) (@@ (gnu packages linux) %default-extra-linux-options)))) or similar, but this may need to be adapted with future Guix versions. If it works at all. Also I suppose you have exactly the same hardware setup as with Trisquel or Debian. For example, I remember something advertised as an HDMI cable but it could not carry sound. Regards, Florian