Q:

What will be the next Yuga after Kali Yuga?

What will be the next Yuga after Kali Yuga?

A:

Traditional answer is Satya Yuga. Many Puranas say Satya, Treta, Dwapara and Kali Yuga occur in cyclic order with no beginning and ending. (Time is cyclic according to Hinduism. Puranas and Vedas assert cyclic nature of time).
 Chapter 29 to 31 ANUSANGA in Brahmanda Purana (Pg- 287-313), Chapter 5 of Kurma Purana and many Puranas describe this cyclic order of four Yugas.
Chapter 31 Anusanga of Brahmanda Purana asserts that Satya Yuga comes after Kali Yuga, by describing change in traits of people from tamas to Satva at end of Kali Yuga.

They were oppressed with old age, sickness and hunger. Owing to misery they reached a stage of abject dejection. From this dejected
  state they reached the state of pondering.Pondering took them
  to the state of equanimity. 
Through the state of Equanimity, they had the realization of Atman.Through this knowledge they acquired piety and devotion. Thus
  those survived the last stage of Kali Yuga acquired tranquility and
  control of sense.
When the close of the Yuga was undergoing transformation,they became quiescent as though they were asleep or inebriated day and
  night after making mind enchanted (and insensible).
Owing to the power of inevitable future, the Krita Yuga set
  in.When the holy Krita Yuga began to function, the subjects pertaining
  to Krita Yuga were born of those who survived from the kali Yuga. Those
  Siddhas who remained then, began to move about invisibly. They
  established themselves there along with seven sages. The Brahmana, the
  kshatriyas,the Vaishyas, and the Sudras were those who were remembered
  as seeds. (They were intended to be the nucleus for the succeeding
  generations). At that they became identical with those who were born
  in the closing stages of Kali.They were devoid of any difference.The
  seven Sages recounted Dharma to them as well as others.

However, Sri Yukteswara Giri in his book The Holy Science expounds reverse cyclic order of Yugas as mentioned in this answer.. But, if we go by Puranas, Satya/Krita Yuga comes after Kali Yuga.

