It is understood his funeral will be held just outside of Wairoa, where he grew up, in the coming days.
Wairoa Mayor Craig Little said Jarreth’s wider family were well known and respected in the community.
“They are good families and it is just tragic,” he said. “It’s affected a lot of people in Wairoa because he has those Wairoa connections and we hold on to those pretty tight.”
Mr Little said Jarreth had moved out of the area and also spent time in the army in the past.
“We have all done something silly in our lives and this one just didn’t work out for him, and it is just tragic for the families and everybody around him.”
A 20-year-old man died jumping from the same crane after a night out in 2015.
Police are assisting the Coroner with inquiries into Jarreth’s death.
“Our thoughts remain with Jarreth’s family and friends,” police said in a statement.
Wellington harbourmaster Grant Nalder said the measures already in place only went so far to deter people from climbing the crane, but it was difficult to know what else could be done.
“It’s very hard without putting a big fence around it and people will still find a way to get around that, I’m sure.
“It’s a tragic accident. There were warning signs not to do it . . . it’s a very unfortunate result.”
Wellington City Council spokesman Richard MacLean said the council had had ongoing discussions with the harbourmaster about ways to prevent people from accessing the vessel.
“We will cooperate with the police and the Coroner over this latest tragedy.
“Our work to instal safety measures along sections of the waterfront is ongoing. This includes balustrades and second-chance barriers and improved lighting.”