Upgrading the crankset - Scott Aspect 960
You have 2 choices: upgrade to a Shimano 2 chainring crank, keep the left shifter, or upgrade to a 3 chainring crank and replace the left shifter with a 3x version.
In both cases the crank must be compatible with '8 speeds'. Sprocket spacing in both the rear cassette and chainrings get progressively narrower as the number of sprockets goes up, and chains get progressively narrower too.
Before you purchase a crank, you need to check that you have clearance between the chainrings and drive-side chainstay. All bike frame have a maximum chainring size they can accommodate. Also check that you can move the front derailleur up slightly to align with the larger rings.
Replacing just the large chainring is not a great idea. Front derailleurs are designed to work with a certain size difference between the chainrings. If you exceed that upshifting will be poor or will not work at all.
Chainring replacement is tricky, there are many ways for rings to be incompatible with cranks. Many lower end cranks do not even have replaceable rings, the rings and spider are a single stamping and riveted together. The crank you linked to has this construction.