There is no successor to Lord Mahavir. He is the 24th and last Tirthankar of this current cycle, and the next Tirthankar will appear in a future cycle.

However, in Jain tradition, Mahavir’s teachings were carried forward by his chief disciples:

• In Śvetāmbar (Shvetambar) tradition: Gautama Swami is regarded as the principal disciple who organized the monks after Mahavir.
• In Digambar (Digambara) tradition: Ganadhar Sudharmaswami is regarded as the senior disciple who helped preserve and propagate Mahavir’s teachings.

If you’d like, I can share brief passages or their roles as described in the Jain sūtras.