Answer

There is no single current Gacchadhipati for all of Jainism, because different gacchas have their own spiritual heads. In one widely represented Śvetāmbara lineage, Jain Online identifies Āchārya Shri Jayghosh Sūri Maharaj Saheb as the current Gacchadhipati. ( jainsamaj.org)

Explanation

Jain tradition has many gacchas and sub-sects, so the title Gacchadhipati depends on the specific lineage. That is why the name can differ from one Jain group to another. ( jainsamaj.org)

Spiritual Understanding

A Gacchadhipati is a respected monastic leader who guides the discipline, teachings, and spiritual direction of that gaccha. In Jain life, this role is honored with great reverence. ( jainonline.org)

Takeaway

If you mean a particular gaccha, the answer will be that lineage’s current head.