In what context?
Gradually reducing something (like doses of medication) over time, is often called tapering down, (sometimes, tapering off), so logically we might expect gradually increasing something to be tapering up.
Oddly, I've never heard that.
However, "ramping up" is widely used in the context of gradually increasing something, for example, Tesla is ramping up production of its new car.
For something physical you can simply turn round and look at from the other end, I think "taper" is OK but I agree "taper up" is a little strange, perhaps "widen" or "thicken" at one end is better.