Learn Hardcore Chinese: jīntiān zhōngwǔ yǐhòu wǒ cái yǒu shíjiān.

It marks not until / only then. It implies the time is later than expected or that earlier times are not available. So the sentence means you won’t have time until after noon today.

What changes if I remove 才?

今天中午以后我有时间: neutral statement, “I have time after noon today” (maybe also earlier).
今天中午以后我才有时间: “Not until after noon today do I have time” (earlier times are ruled out and there’s a slight sense of lateness).

Where should 才 be placed?

Put 才 right before the verb phrase it modifies: 我才有时间. You can say:

今天中午以后我才有时间
我今天中午以后才有时间 But not: ✗ 今天中午以后才我有时间.

Can the time phrase go after the subject?

Yes. Both are natural:

今天中午以后，我才有时间. (time fronted for topic/emphasis)
我今天中午以后才有时间. (default Subject + Time order)

Do I need a comma after 今天中午以后?

Optional. In writing, a comma is common after a long fronted time phrase: 今天中午以后，我才有时间.

What’s the difference between 中午以后 and 下午?

中午以后: “after 12:00,” potentially including afternoon and evening.
下午: specifically “afternoon.” If you only mean the afternoon, say 我下午才有时间.

How do 以后, 之后, and 后来 differ?

以后 and 之后 both mean “after.” 之后 sounds a bit more formal; both work with a specific anchor: 今天中午以后/之后.
后来 is “later (afterwards)” in a narrative sequence and is not used with a specific anchor like 今天中午后来✗.

Can 以后 mean “in the future”?

Yes. With no specific anchor, 以后 means “from now on/in the future,” e.g., 以后我多练习汉语.

Why use 有 with 时间? Why not another verb?

有时间 literally means “to have time,” which is how Mandarin expresses being free/available. A common colloquial synonym is 有空.

Should I add 会 to indicate the future?

Not required. Schedules and near-future plans often use the simple present in Chinese. 我今天中午以后才会有时间 is also fine; 会 adds a predictive feel.

Should I add 了 anywhere?

Usually no. If you’re describing a change that has already happened, you could say sentence-final 了: 今天中午以后我才有时间了 (implies that after noon, the situation has changed). For future plans, don’t add 了.

How do I say the opposite (earlier than expected)?

Use 就 (jiù):

今天早上我就有时间: “I already have time in the morning (earlier than expected).” Compare with 才 for later than expected:
今天中午以后我才有时间.

How do I say “before noon” instead?

Use 以前/之前:

今天中午以前我有时间.
今天中午之前我有时间. Both mean “I have time before noon today.”

Can I use the 只有…才… pattern here?

Yes, for emphasis/condition:

只有今天中午以后我才有时间. It stresses that only in that time window will you have time.

Is there a cleft form with 是…才…的 to emphasize?

Yes, especially to explain or correct someone:

我是今天中午以后才有时间的. This highlights and confirms the specific time window.

How would I ask this as a question?

你今天中午以后才有时间吗? (Yes–no question)
你几点以后才有时间? (Wh-question: “After what time do you have time?”)

How do I specify how much time I have?

Add a duration:

今天中午以后我才有两个小时的时间/空. (“I only have two hours after noon today.”)

Is 中午以后 the same as “after lunch”?

Not necessarily. 中午以后 is “after 12:00.” If you mean after you finish eating, say 吃完午饭以后 or 午饭以后.

What’s the full pinyin and any pronunciation tips?

Jīntiān zhōngwǔ yǐhòu wǒ cái yǒu shíjiān.

才 cái (2nd tone), 有 yǒu (3rd), 时间 shíjiān (2nd + 1st).
Speak smoothly with a slight pause after the long time phrase if you like.

Any other natural variants?

要到/直到今天中午以后我才有时间. (emphasizes “not until”)
今天中午以后我才有空. (colloquial 有空)