SECURITIESAND EXCHANGE COMMISSION

Washington,D.C. 20549

FORM6-K

REPORTOF FOREIGN PRIVATE ISSUER

PURSUANTTO RULE 13a-16 OR 15d-163

UNDERTHE SECURITIES EXCHANGE ACT OF 1934

Forthe month of July 2025

AlterityTherapeutics Limited

(Nameof Registrant)

Level 14, 350 Collins Street,Melbourne, Victoria 3000 Australia

(Addressof Principal Executive Office)

Indicateby check mark whether the registrant files or will file annual reports under cover of Form 20-F or Form 40-F.

Form20-F ☒       Form 40-F ☐

ThisForm 6-K is being incorporated by reference into our Registration Statement on Form S-8 (Files No. 333-251073, 333-248980and 333-228671) and ourRegistration Statements on Form F-3 (Files No. 333-274816, 333-251647, 333-231417and 333-250076)

ALTERITYTHERAPEUTICS LIMITED

(adevelopment stage enterprise)

Thefollowing exhibits are submitted:

SIGNATURE

Pursuantto the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf bythe undersigned, thereunto duly authorized.

Date:July 21, 2025

Exhibit 99.1

Appendix 2A - Application for quotation of securities

AnnouncementSummary

Entityname

ALTERITYTHERAPEUTICS LIMITED

AnnouncementType

Newannouncement

Dateof this announcement

Monday July 21, 2025

The+securities to be quoted are:

+Securities issued, transferred or re-classified as a result of options being exercised or other +convertible securities being converted

Totalnumber of +securities to be quoted

Referto next page for full details of the announcement

Appendix 2A - Application for quotation of securities

Part1 - Entity and announcement details

1.1Name of entity

ALTERITYTHERAPEUTICS LIMITED

We(the entity named above) apply for +quotation of the following +securities and agree to the matters set out in Appendix 2A of the ASXListing Rules.

1.3ASX issuer code

ATH

1.4The announcement is

Newannouncement

1.5Date of this announcement

21/7/2025

Appendix 2A - Application for quotation of securities

Part2 - Type of Issue

2.1The +securities to be quoted are:

+Securitiesissued, transferred or re-classified as a result of options being exercised or other +convertible securities being converted

2.2The +class of +securities to be quoted is:

Additional+securities in a class that is already quoted on ASX (“existing class”)

Appendix 2A - Application for quotation of securities

Part 3B - numberand type of +securities to be quoted (existing class) where issue has not previously been notified to ASX in an

Appendix3B

Existing+securities converting into additional +securities in an existing class

FROM(Existing Class)

ASX+security code and description

ATHO : OPTION EXPIRING 31-AUG-2026

TO(Existing Class) 

ASX+security code and description

ATH: ORDINARY FULLY PAID

Is thisall of the options or other +convertible securities on issue of that type (ie have all of those options now been exercised or have allof those convertible securities now been converted)? 

No

Theright of the holder of the options or other +convertible securities to receive the +underlying securities is being satisfied by:

Anissue of new +securities

Theunderlying +securities being received by the holder are:

Intendedto be, but are not yet, quoted by ASX 

Werethe options being exercised or other +convertible securities being converted issued under an +employee incentive scheme?

No

Issuedate

16/7/2025 

Willthe +securities to be quoted rank equally in all respects from their issue date with the existing issued +securities in that class?

Yes

Appendix 2A - Application for quotation of securities

Issuedetails

Numberof +securities to be quoted 

95,238

Arethe +securities being issued for a cash consideration?

Yes

Anyother information the entity wishes to provide about the +securities to be quoted

Appendix 2A - Application for quotation of securities

Part 4 -Issued capital following quotation

Followingthe quotation of the +securities the subject of this application, the issued capital of the entity will comprise:

The figures in parts 4.1 and 4.2 below are automatically generated and may not reflect the entity’s current issued capital if other Appendix2A, Appendix 3G or Appendix 3H forms are currently with ASX for processing.

4.1Quoted +securities (total number of each +class of +securities quoted on ASX following the +quotation of the +securities subject of thisapplication)

4.2Unquoted +securities (total number of each +class of +securities issued but not quoted on ASX)