Opposite of "mute" or "silence" as verb
Solution 1:
For televisions and similar appliances unmute is an acceptable word that is in common usage.
For silence meaning subdue I would choose encourage as an antonym .
Solution 2:
Despite what your dictionary might say (or not say),
unmute
is a perfectly acceptable word to describe that action. There are many combinations of affixes that are productive on many roots which just aren't mentioned in word lists.
Solution 3:
Oh, there won't be a special word. So many people watch tv with others, there's only one remote. We'd all be using it if there was such a word.
reinstate is a single-word that could sometimes be used.
In the context of the tv scenario, I'd just say put it back, or turn the sound back on, or something. I certainly wouldn't unmute it.