Add another photo of my tree.

Hello albertkao, in general I would say make a proper pruning cut about an inch off the trunk.

Since nothing needs done immediately I may as well ask a few questions. It seems a stretch to imagine why we would not want to trim that dead branch off though unless you see buds forming or opening on it.

I tried to zoom in on the first picture and it looks like the branch has been dead for some time. Is that correct?

When was it planted?

What type of tree is it and what is the white stuff around the bottom?

Any reason you can think of for why the branch is dead? Drought?