Learn Hardcore Japanese: yuugake wo suru. - I apply glaze to the pottery.

A common reading is ゆうがけ. In pottery-related Japanese, you may also see or hear less compact expressions such as 釉薬を掛ける or うわぐすりをかける. The main thing to notice here is that 釉掛け is the name of the process: glazing or applying glaze.

Why does the sentence use をする?

Because 釉掛け is being treated like an action noun.

The pattern is:

X をする = to do X

So:

釉掛けをする = to do glaze application / to do the glazing

This is the same basic structure as:

勉強をする = to study
掃除をする = to clean

Why not just say 釉を掛ける?

You can, and the nuance is slightly different.

釉を掛ける focuses more directly on the act of applying glaze to something.
釉掛けをする treats the whole thing as a named task or process.

So the difference is similar to:

apply glaze vs.
do the glazing

Both can be natural, depending on context.