There could be a small clash where both sides would have to step in to calm the situation (most likely scenario). Small scuffles are common in the region. India is standing ground due to backing of Washington's strategy to curb China's gaining influence around the World. India wouldn't stand its ground alone. A large clash will be a big loss to both sides financially and would be stupid in simple words.

Hypothetically if clashes slowly reaches toward the western border and turns into a war, Pakistan will certainly get involved. Currently for China it is not an issue about the physical border it is about India stepping in where they shouldn't. For Indias nationalist government it is about showing resiliency to a bigger fish. The matter is actually inside Bhutan from reading so far. Currently it is a psychological battle ground more than a physical. Pakistan surely wouldn't sit around if clashes take place. Mostly these small things get sorted out through dialogue and everyone forgets. I wouldn't bet on anything big but you may never know about the "secrets" of geopolitics.