أحتاج إلى نظرة أخرى.

A careful pronunciation is:

aḥtāju ilā naẓratin ukhrā

A few helpful notes:

• أحتاج = aḥtāju
• إلى = ilā
• نظرة = naẓrah in pause, but here it connects to the next word, so you hear naẓrat-
• أخرى = ukhrā

So in connected speech, نظرة أخرى sounds like naẓratin ukhrā in fully inflected reading.

Because the verb أحتاج already includes the subject I.

In Arabic, verb forms usually show who is doing the action. So:

• أحتاج = I need
• تحتاج = you need or she needs depending on context
• يحتاج = he needs

You can add أنا and say أنا أحتاج إلى نظرة أخرى if you want emphasis, but it is not necessary.

In Modern Standard Arabic, the verb احتاج is commonly used with the preposition إلى.

So the pattern is:

• احتاج إلى شيء = to need something

That means:

• أحتاج إلى مساعدة = I need help
• أحتاج إلى وقت = I need time
• أحتاج إلى نظرة أخرى = I need another look

Even though English says need something with no preposition, Arabic normally uses إلى after this verb.

نظرة is a noun meaning a look, a glance, or an examination/look at something, depending on context.

It comes from the root ن ظ ر, which is connected with looking or seeing.

In this sentence, it is the thing that is needed:

• أحتاج = I need
• إلى نظرة = a look

So the whole phrase means I need another look.

Because in Arabic, adjectives normally come after the noun they describe.

So:

• نظرة أخرى = literally a look other
• natural English = another look

This is very normal Arabic word order:

• كتاب جديد = a new book
• سيارة كبيرة = a big car
• نظرة أخرى = another look

Because نظرة is a feminine noun, so the adjective must also be feminine.

• masculine: آخر
• feminine: أخرى

Since نظرة is feminine, Arabic says:

• نظرة أخرى

If the noun were masculine, you would use آخر instead:

• رأي آخر = another opinion
• كتاب آخر = another book

Arabic does not have a separate word for a/an.

Instead:

• an indefinite noun usually has no ال
• a definite noun usually has ال

So:

• نظرة أخرى = another look / a different look
• النظرة الأخرى = the other look

Here the phrase is indefinite, so there is no ال.

In fully vocalized Modern Standard Arabic, you could write:

أحتاجُ إلى نظرةٍ أخرى

Why?

• أحتاجُ ends in -u because it is a present-tense verb in a normal indicative form.
• إلى is a preposition.
• The noun after a preposition is usually genitive, so نظرة becomes نظرةٍ.

In everyday writing, those short vowels are usually omitted, so you normally just see:

أحتاج إلى نظرة أخرى

It depends on whether the word is connected to what follows.

• If you stop on the word by itself, it is usually pronounced like -ah:
  نظرة → naẓrah
• If another word follows and it is grammatically connected, the t sound appears:
  نظرة أخرى → naẓrat... ukhrā

So in this sentence, you normally hear the t because نظرة is followed by أخرى.

Yes. That is perfectly correct.

The difference is mostly emphasis:

• أحتاج إلى نظرة أخرى = neutral, natural
• أنا أحتاج إلى نظرة أخرى = I need another look, with extra emphasis on I

Arabic often leaves out the subject pronoun when the verb already makes it clear.