Milestone Payment Liability - Schedule of Milestone Payment Liability (Details) - USD ($) $ in Thousands	12 Months Ended
Jun. 30, 2024	Jun. 30, 2023
Business Combinations [Abstract]
Balance	$ 166	$ 163
Change in fair value estimate	20	3
Balance	$ 186	$ 166

Milestone payment liability change in fair value estimate.

No definition available.

Name:	ktra_MilestonePaymentLiabilityChangeInFairValueEstimate
Namespace Prefix:	ktra_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration