According to Jainism, the tradition of Tirthankaras is well-defined. Jain scriptures state that there will be a total of 24 Tirthankaras in the current time cycle (Avasarpini), and all 24 have already appeared, with Lord Mahavira being the 24th and last Tirthankara of this era.

However, Jain cosmology also describes that in the next time cycle (Utsarpini), there will again be Tirthankaras. Specifically, it is mentioned that in the next Utsarpini, the first Tirthankara will be Shri Padmanabh (in Digambara tradition) or Shri Mahapadma (in Śvetāmbara tradition), and his father will be King Shreedhar (or Sreedhar).

To summarize:

• Next Tirthankara (in next Utsarpini): Padmanabh (Digambara) / Mahapadma (Śvetāmbara)
• His Father: King Shreedhar (Sreedhar)

This information is based on Jain scriptures such as "Tiloyapannatti" and "Trilokasara."