The sentence in question:
"It's high time" - is a formal statement that it is important that something happen soon or that something happen now.
That's exactly right. With third-person singular nouns, we should always use the third-person singular forms of verbs. In other words, our verbs must end in s. That's all true, but not in this case! What we've got here is called a subjunctive mood (or just a subjunctive for short). Here's a quote from the Wikipedia article on the subjunctive as it's used in English:
The subjunctive in English is used to form sentences that do not describe known objective facts. These include statements about one's state of mind, such as opinion, belief, purpose, intention, or desire. The subjunctive mood, such as She suggests that he speak English, contrasts with the indicative mood, which is used for statements of fact, such as He speaks English.
With subjunctives, we always use bare infinitives (e.g. run is the bare infinitive of the verb to run). The English subjunctive is a rather complex and messy topic. It comes in many different shapes and forms (May God rest his soul is an example of the English subjunctive). For more information, see that Wikipedia article I provided. The only thing I'll add is that the English subjunctive is going to be easy for you in 90% of the time if you remember at least these two grammar patters:
it is important that someone do something
someone demands that someone do something.
It is important that she be here before noon.
Russia demands that the UK extradite 61 people who are accused of committing economic crimes in their homeland.