[est]

I wonder if there's a chip that gathers time from LTE and GPS signals and time only.

No complete protocol or handshake, just grab some close-enough time.

[s17tnet]

This is discussed here [0]. It is possible and there are a couple of options but there are some catches: LTE is UTC only, GNSS requires much power.

[0] https://www.eevblog.com/forum/chat/cheapest-way-to-get-datet...