التحقيق يسبق شهادة السلامة.

It would typically be written:

التَّحْقِيقُ يَسْبِقُ شَهَادَةَ السَّلَامَةِ

The case endings are:

• التَّحْقِيقُ = nominative, because it is the subject
• يَسْبِقُ = imperfect verb
• شَهَادَةَ = accusative, because it is the direct object
• السَّلَامَةِ = genitive, because it is the second part of an iḍāfa construction

In normal unvowelled writing, these endings are usually not shown.

Yes. التحقيق is the subject.

The structure is basically:

• التحقيق = the investigation / inspection / verification
• يسبق = precedes
• شهادة السلامة = the safety certificate

So التحقيق is the thing doing the action of preceding.

Because it agrees with التحقيق, which is grammatically singular and masculine.

يَسْبِقُ means he/it precedes. In Arabic, non-human nouns still take normal grammatical gender, and تحقيق is treated as masculine singular.

So the verb is singular masculine because its subject is singular masculine.

Arabic allows both patterns:

• التحقيق يسبق شهادة السلامة
• يسبق التحقيق شهادة السلامة

Both are possible.

When the noun comes first, it often feels more like The investigation precedes the safety certificate, with a bit more focus on the investigation as the topic.

When the verb comes first, the sentence is more straightforwardly verbal in style.

In this sentence, starting with التحقيق is completely natural.

Because شهادة السلامة is an iḍāfa construction, often called a genitive construction or annexation.

In an iḍāfa:

• the first noun usually does not take الـ
• the second noun determines whether the whole phrase is definite

So:

• شهادة = certificate
• السلامة = the safety
• شهادة السلامة = the safety certificate

Even though شهادة has no الـ, the whole phrase is definite because السلامة is definite.

Because it is the second term of the iḍāfa:

• شهادةُ السلامةِ
• شهادةَ السلامةِ
• شهادةِ السلامةِ

No matter what case the first noun takes in the larger sentence, the second noun in an iḍāfa is genitive.

Here, شهادة is the direct object, so it is accusative: شهادةَ.
But السلامة stays genitive: السلامةِ.

Because يسبق takes a direct object.

In English, precede also works directly:

• The investigation precedes the safety certificate

So in Arabic:

• يسبق شهادةَ السلامةِ

There is no need for a preposition like before here, because the verb itself already carries that meaning.

The whole phrase شهادة السلامة is the direct object of يسبق.

Inside that phrase:

• شهادة is the first noun of the iḍāfa
• السلامة is the second noun of the iḍāfa

So the phrase has two levels of grammar:

1. In the full sentence, شهادة السلامة functions as the object.
2. Internally, السلامة depends on شهادة in an iḍāfa relationship.

يسبق comes from the root س-ب-ق, which is connected with the idea of coming before, preceding, or being ahead.

Its basic past-tense form is:

• سَبَقَ = he/it preceded

Its imperfect form here is:

• يَسْبِقُ = he/it precedes

This is a basic Form I verb.

It is a verbal noun (maṣdar).

تحقيق comes from the verb حَقَّقَ, which can mean things like:

• to verify
• to investigate
• to establish
• to ascertain

So تحقيق can mean:

• investigation
• verification
• inspection, in some contexts

Even though it is a verbal noun, it behaves like an ordinary noun in the sentence:

• it can take الـ
• it can be the subject
• it can take case endings

Yes. تحقيق is a context-sensitive word.

Depending on the setting, it can mean:

• investigation
• verification
• inspection
• inquiry

So in a legal context, التحقيق may mean the investigation.
In a technical or administrative context, it might be closer to the inspection or the verification.

That is very common in Arabic: one noun may have several related English translations, and the correct one depends on context.

In formal reading, you might hear:

التَّحْقِيقُ يَسْبِقُ شَهَادَةَ السَّلَامَةِ

But in less careful pronunciation, especially outside very formal recitation, speakers often reduce or omit the final case vowels, so it may sound more like:

التَّحْقِيق يَسْبِق شَهَادَة السَّلَامَة

The grammatical structure is still the same; the difference is mainly in how fully the endings are pronounced.

Yes, slightly.

Compare:

• التحقيق يسبق شهادة السلامة
• يسبق التحقيق شهادة السلامة

Both mean the same thing in a basic sense, but the first version gives a little more prominence to التحقيق by placing it first as the topic.

For a learner, the most important point is that both are grammatical, and the sentence you were given is a very natural way to say it.