Learn Arabic (Modern Standard): هاتفه جديد.

In Arabic, possessive words like "his", "my", or "your" are not separate words. They are attached to the end of the noun as a suffix. Here, the suffix ـه attached to هاتف (phone) means "his", making هاتفه (his phone).

How is the attached pronoun ـه pronounced here?

The suffix for "his" is generally pronounced "-hu". So the full word هاتفه is pronounced "haatifuhu". However, in spoken Arabic or when pausing at the end of a sentence, the final short vowel is often dropped, making it sound like "haatifuh".

Where is the word for "is" in this sentence?

Arabic does not use a "to be" verb like "is" or "are" in present tense sentences. You just say the subject (هاتفه, his phone) followed directly by the description (جديد, new), and the "is" is automatically understood.

Would the word for "new" change if we were talking about her phone instead of his?

No, the adjective جديد (new) describes the phone itself, which is a masculine noun (هاتف). Even if we say هاتفها (her phone), the phone remains masculine, so the adjective stays masculine. You only change the adjective to feminine if the object itself is a feminine word.