The bandwidth of a network card would generally outclass your internet connection by an order of magnitude.

Gigabits per second network cards have been standard for at least a decade.

And then there’s your wifi too, if applicable, but even that is much faster than your general internet connection, unless you’re far from your router. A new laptop might help you get a better wifi signal, if it had a newer wifi protocol or stronger radio, but that’s also going to depend on your router.

But in front of all of that is going to be your modem. Depending on the quality of your modem that might be a bottleneck.