Police are seeking 20-year-old Jahrome Simon, who has a warrant to arrest for conspiring to pervert the course of justice.
He is believed to be visiting areas including Whanganui, Palmerston North and Hamilton.
Simon should not be approached, police said in a statement.
Anyone with information is asked to contact 105 and ask to speak to the Operation Skyline team, or quote file number 210304/6009.
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Alternatively Crimestoppers can be contacted anonymously on 0800 555 111.
Operation Skyline is the investigation into the killing of Rau Tongia in the Wellington suburb of Karori on December 20.
Earlier this week police said they were making good progress and were not ruling out further arrests or charges.
Inquiries continued to be made in relation to the firearm recovered in the investigation.
Police were especially interested in understanding who had the firearm in the days and weeks prior to the shooting.
They were also continuing to investigate whether there were others involved on the night.