When you start yawning widely, you know it’s time to get some rest.

which word is the possessive adjective?

"It's" is the possessive adjective.

Explanation:

Possessive adjectives are those words that show the possessive nature/ form of the noun. They modify the noun, making the sentences more fluid. These possessive adjectives will or can be detected by their use of ('s) in the words/ pronouns they are associated to.

In the sentence that is provided in the question,

When you start yawning widely, you know it’s time to get some rest

the word "it's" shows the possessive adjective of the noun "time'. So, the possessive adjective in the sentence is "It's".