The Subjunctive

"I suggest that he have everything ready ahead of time."

The question is why the verb have is used instead of has:

The sentence you're wondering about is in the subjunctive mood. This is the mood that's used to express wishes, proposals, suggestions, or imagined situations. The subjunctive verb (in this case, have) usually appears in one clause in a sentence while an indicative verb (in this case, suggest) appears in another clause.

Verbs that often (but not always) are followed by a verb in the subjunctive include: advise, insist, propose, require, ask, intend, recommend, suggest, demand, order, regret, urge, desire, prefer, request, and wish.

Here are a few additional examples:

He insisted that she stop smoking.
The governor is demanding that he resign.
They asked that you be on time tomorrow.
We recommend that he be punished.
She wishes the teacher were more helpful.

As you can see, the subjunctive forms look like ordinary past and present verb forms; thus, they are often called the past subjunctive and present subjunctive. These differ from the simple past and simple present in only two ways:

(1) In the present subjunctive, the third-person singular takes no inflection.
(2) The verb be has only two subjunctive forms: be for the present subjunctive (as in the third and fourth sentences) and were for the past subjunctive (as in the last sentence).

The present subjunctive actually refers mostly to the future. It is generally used in a clause beginning with that (though that may often be omitted):

She suggested (that) he arrive early.
He desires that the carpenter leave space for another bookcase.

The past subjunctive may refer to the present or the past. Like the present subjunctive, it often occurs in a that-clause:

I wish (that) you loved me.
She wishes (that) she were younger.
They talked about him as if he weren't even in the room.

The English subjunctive has always been used inconsistently. Native English-speakers often use "should" instead of the present subjunctive and use "was" instead of the past subjunctive's were:

She suggested (that) he should arrive early.
He desires that the carpenter should leave space for another bookcase.
She wishes she was younger.
They talked about him as if he wasn't even in the room.

As for the first sentence above, some native English-speakers would prefer:

"I suggest that he should have everything ready ahead of time."