אם התושבת החדשה תביא לעירייה גם את הביטוח וגם את המסמך עם החותמת, הפקחית תוכל לעזור לה מהר יותר.

אם means if and introduces the condition.

So the sentence has this basic structure:

• אם ... = if ...
• ..., הפקחית תוכל ... = ..., the inspector/official will be able ...

Hebrew often puts the if-clause first, just like English can:
If X happens, Y will happen.

Because in Hebrew, a real future condition usually uses the future tense in the if-clause too.

So Hebrew says:

• אם התושבת החדשה תביא ... = if the new resident brings / will bring ...

Even though English often uses the present in this kind of sentence (if she brings), Hebrew normally uses the future form: תביא.

The form תביא can sometimes mean she will bring or you will bring depending on context. Here the subject is explicitly stated:

• התושבת החדשה = the new female resident

Since that subject is feminine singular, תביא is understood as she will bring.

In Hebrew, adjectives usually come after the noun they describe.

So:

• תושבת חדשה = a new resident
• התושבת החדשה = the new resident

This is normal Hebrew word order. English usually does adjective + noun, but Hebrew usually does noun + adjective.

Because in Hebrew, if a noun is definite, its adjective must also be definite.

So:

• תושבת חדשה = a new resident
• התושבת החדשה = the new resident

This is a very important rule: adjectives agree with the noun in:

• gender
• number
• definiteness

את is the marker of a definite direct object. It usually is not translated into English.

Here:

• את הביטוח = the insurance
• את המסמך = the document

Hebrew uses את because both objects are definite: they have ה־.

If the nouns were indefinite, את would normally disappear:

• להביא ביטוח = to bring insurance
• להביא את הביטוח = to bring the insurance

Because each definite direct object gets its own את.

So Hebrew says:

• גם את הביטוח וגם את המסמך

not just one את for both.

This structure is very natural in Hebrew when listing definite objects.

גם ... וגם means both ... and ... or sometimes also ... and also ....

Here it links the two things that must be brought:

• גם את הביטוח וגם את המסמך = both the insurance and the document

This is a very common Hebrew pattern.

The ל־ prefix means to or for.

So:

• עירייה = municipality / city hall
• לעירייה = to the municipality / to city hall

Hebrew very often attaches short prepositions directly to the word:

• ל = to
• ב = in
• כ = as/like
• מ = from

So instead of writing a separate word for to, Hebrew usually attaches it.

It describes המסמך.

So the phrase means:

• the document with the stamp/seal

In Hebrew, a phrase like עם החותמת comes after the noun it describes, just like many other modifiers do.

So the structure is:

• את המסמך עם החותמת = the document with the stamp

Because פקחית is a feminine noun. It is the feminine form of פקח.

So:

• פקח = a male inspector/official
• פקחית = a female inspector/official

That is why the next verb is also feminine singular:

• הפקחית תוכל = the female inspector/official will be able

Hebrew expresses can / be able to with a conjugated form of יכול plus an infinitive.

So:

• תוכל = she will be able
• לעזור = to help

Together:

• תוכל לעזור = she will be able to help

This is the normal Hebrew way to say can help or will be able to help.

Because the verb לעזור normally takes ל־ for the person being helped.

So Hebrew thinks of it more like:

• to help to someone

That gives:

• לעזור לה = to help her

Here לה refers back to התושבת החדשה.

This is a very useful thing to memorize:
לעזור ל־מישהו / ל־מישהי = to help someone

מהר יותר means more quickly or faster.

Yes, Hebrew can also say יותר מהר. Both are common.

• מהר יותר = a bit more neutral/formal-sounding
• יותר מהר = very common in everyday speech

In this sentence, it modifies the helping:

• תוכל לעזור לה מהר יותר = she will be able to help her faster

The comma separates the condition from the main result:

• אם ... , ...
• if ..., then ...

So the first part gives the condition:

• אם התושבת החדשה תביא ...

and the second part gives the result:

• הפקחית תוכל לעזור לה מהר יותר

This punctuation works very much like English.