Answer : 3. "worked"
Explanation :

In the past tense, we use the second form of the verb (V2).

In the above sentence, Palak has already worked in different schools, after that

decision is made.

Thus, we will use past these to complete the sentence.

The complete sentence is- Having worked in both government and private schools,

Palak is the most suitable person to take over as the principal of the school.