Learn Turkish: Mesleği çok zor. - His profession is very hard.

When a word ends in k and you add a suffix that starts with a vowel, the k usually softens into a yumuşak g (ğ). Here, adding the possessive suffix -i changes meslek to mesleği.

Where is the word for his in this sentence?

In Turkish, you often don't need to say the word for his (onun) because the possessive suffix at the end of the noun already shows who owns it. The -i in mesleği tells us it belongs to him, her, or it.

The lesson mentioned a buffer s for the 3rd person possessive. Why isn't it mesleksi?

The buffer letter s is only used when the noun ends in a vowel, for example, araba becomes arabası. Since meslek ends in a consonant, we just attach the vowel suffix -i directly.

Could Mesleği çok zor also mean her profession is very hard?

Yes! Turkish doesn't have gender pronouns. The suffix -i and the hidden pronoun onun can mean his, her, or its. You would know which one it is from the context of the conversation.