فوق المكتب ساعة، وتحتها ورقة فيها عنوان جديد.

In Arabic, especially in the present tense, you often do not use a verb for to be.

So فوق المكتب ساعة literally looks like above the desk a clock, but the natural meaning is There is a clock on the desk or A clock is on the desk.

This is very common in Arabic:

• في البيت رجل = There is a man in the house
• على الطاولة كتاب = There is a book on the table

So the sentence is perfectly normal without a separate word for is.

Starting with the place expression is a very common Arabic way to introduce something that exists somewhere.

• فوق المكتب ساعة = There is a clock/watch on the desk
• الساعة فوق المكتب = The clock/watch is on the desk

The difference is important:

• فوق المكتب ساعة introduces a new item
• الساعة فوق المكتب talks about the clock/watch, something already known

So this word order helps create the meaning of there is.

Because the sentence is talking about:

• المكتب = the desk, a specific desk
• ساعة = a clock/watch, not previously identified
• ورقة = a paper/sheet, also not previously identified

In Arabic, this is a very common pattern:

• a known place is definite
• the thing being introduced is indefinite

So فوق المكتب ساعة means there is a clock/watch on the desk, not the clock/watch.

They are words of location, often called adverbs or nouns of place in grammar explanations.

• فوق = above / over / on top of
• تحت = under / beneath

In this sentence:

• فوق المكتب = above/on the desk
• تحتها = under it

In full grammatical Arabic, these are often treated as ظروف مكان (expressions of place).

The ending -ها means her / it for a feminine singular noun.

So:

• تحتها = under her/it

Here it refers to ساعة, because ساعة is a feminine noun in Arabic.

So the meaning is:

• فوق المكتب ساعة = there is a clock/watch on the desk
• وتحتها ورقة = and under it there is a paper

A useful contrast:

• تحته would mean under him/it for a masculine noun
• تحتها means under her/it for a feminine noun

Because the pronoun is feminine singular: ها.

But المكتب is masculine, so if it referred to المكتب, Arabic would use تحته.

Since ساعة is feminine, تحتها naturally refers to ساعة.

So the grammar tells you the reference:

• المكتب → masculine → تحته
• ساعة → feminine → تحتها

فيها means in it.

It refers to ورقة, because ورقة is feminine singular.

So:

• ورقة فيها عنوان جديد literally = a paper, in it a new address
• natural English = a paper with a new address on it or a paper containing a new address

So the first pronoun in تحتها refers back to ساعة, but the second pronoun in فيها refers to ورقة.

This is a normal difference between the two languages.

Arabic often uses في in places where English might prefer on, especially when talking about content written in a document or paper.

So:

• فيها عنوان جديد literally = in it is a new address
• natural English = there is a new address on it

This is not strange in Arabic; it is just a different way of conceptualizing written content.

Because ورقة is indefinite.

After an indefinite noun, Arabic can describe it with a whole sentence directly, without using التي.

So:

• ورقة فيها عنوان جديد = a paper that has a new address on it

This is a very common Arabic structure.

Compare:

• ورقة فيها عنوان جديد = a paper that has a new address
  indefinite noun, so no التي

• الورقة التي فيها عنوان جديد = the paper that has the new address
  definite noun, so التي is used

Because جديد is describing عنوان, and عنوان is masculine singular.

Adjectives in Arabic agree with the noun they describe in gender and number.

So:

• عنوان جديد = a new address
  masculine singular noun + masculine singular adjective

If the noun were feminine, the adjective would also be feminine:

• ورقة جديدة = a new paper
• ساعة جديدة = a new clock/watch

So جديد is correct because it matches عنوان, not ورقة.

Because عنوان is indefinite, so its adjective must also be indefinite.

In Arabic, adjectives match the noun in definiteness too.

So:

• عنوان جديد = a new address
• العنوان الجديد = the new address

The same rule applies throughout Arabic:

• كتاب مفيد = a useful book
• الكتاب المفيد = the useful book

A fully vowelled version would be:

فوقَ المكتبِ ساعةٌ، وتحتَها ورقةٌ فيها عنوانٌ جديدٌ.

A few useful notes:

• فوقَ and تحتَ take fatḥa here
• المكتبِ has kasra
• ساعةٌ، ورقةٌ، عنوانٌ، جديدٌ are indefinite and would normally take tanwīn

In normal everyday writing, these short vowels are usually omitted, so you see: فوق المكتب ساعة، وتحتها ورقة فيها عنوان جديد.

Yes, you could.

• هناك ساعة فوق المكتب = There is a clock/watch on the desk
• فوق المكتب ساعة = also There is a clock/watch on the desk

The version with هناك makes the existential idea more explicit.
The original sentence is a little more compact and very natural in written MSA.

Also compare:

• الساعة فوق المكتب = The clock/watch is on the desk
• فوق المكتب ساعة = There is a clock/watch on the desk

So the original sentence is specifically good for introducing new objects in a location.