To answer the question about which athlete set a new record in triple jump with a 15.66 m leap at the 2025 Khelo India Youth Games, we need to evaluate the given options and select the correct one.

1. The question provides four athletes:
   1. Qadir Khan
   2. Animesh Kujur
   3. Tushar Chaudhary
   4. Sheikh Zeeshan
2. The question specifies that this record-setting event occurred at the Khelo India Youth Games in May 2025, and we are looking for the athlete who achieved a 15.66 m leap in the triple jump event.
3. According to the provided information, the correct answer is "Sheikh Zeeshan," who set a new record with a 15.66 m leap in the event.
4. Let's quickly consider why the other options may not be correct:
   1. Qadir Khan - There is no mention of him setting a triple jump record in the provided context.
   2. Animesh Kujur - Similarly, no records of a triple jump achievement at the event are associated with him.
   3. Tushar Chaudhary - Does not seem to have set the triple jump record either as per the specifics given.
5. Thus, given the context and the options, Sheikh Zeeshan is the athlete who achieved the 15.66 m leap at the 2025 Khelo India Youth Games, setting a new triple jump record.

Therefore, the answer is Sheikh Zeeshan.