The assault took place on Harehills Road, close to the junction with Bexley Terrace at about 11.05pm on Friday, July 15.
A man in his thirties received hospital treatment for wounds to his neck, police confirmed.
A 32-year-old man who was arrested in connection with the incident has been released under investigation for enquiries to continue.
Anyone who recognises the man in the image, or who can assist with the investigation, is asked to contact Leeds District CID on 101 or by using the Livechat facility on the West Yorkshire Police website.
The crime reference is 13220386350 for the incident.
Information can also be reported anonymously to the independent charity Crimestoppers on 0800 555111 or online.