Is it possible to consolidate Virgin (Velocity) with AirNZ Airpoints?

TL;DR - No, but you probably don't need to

As a general rule, most airline programs accept inbound transfers, but don't support sending miles out. Except for a few special cases, once the miles are in your airline loyalty program, your only sensible option is to spend them from there

(Some programs do let you transfer your points to someone else, but normally with very high fees that are rarely worth while. A few programs let you transfer out, often to hotel programs, but almost always at very poor rates so you'd loose 90-odd % of your miles in the process)

There are a handful of exceptions though, and Virgin Australia is one of those! But not in a way that helps you... You can transfer (for a small penalty) to Singapore Airlines, see this blog for a good overview, or the terms and conditions. You'll pay 1.35 velocity points per 1 KrisFlyer mile you get, or the other way round 1.35 KrisFlyer for 1 velocity point.

What you can do is top up your AirNZ and Virgin Australia Velocity balances from elsewhere. You can transfer in from a few hotel programs, and a few credit card programs, and a few shopping programs. Since I think you're in Australia at the moment, look at ANZ Reward Points, FlyBuys and the like.

Your aim here is to get up enough points in each for a one-way ticket, probably within Australia or New Zealand. You can then redeem your Virgin points one way, AirNZ for the return leg.

Then, when you're all done, pick just one program of the two, and credit all your future flights there wherever you can!

Unfortunately, you have a couple of strikes against you.

1. It has always been almost next to impossible to transfer points directly from one airline program to another, and nowadays it is difficult to transfer them out at all. A telling sign is the dwindling list of options on the WebFlyer Mileage Converter calculator.
2. Air New Zealand is tight-fisted. For example, Starwood Preferred Guest Starpoints convert to ANZ Airpoints at a 65:1 ratio (granted, an Airpoint is not equivalent to a frequent flyer mile).

It is not possible to transfer Velocity points into any credit card or hotel program, or to Points.com, which closes out the customary back doors. So depending on your accrual and spending patterns, you could consider topping off the Velocity account until you can make a redemption (perhaps with a retail partner), or, as Gagravarr notes, take the opportunity to transfer Velocity Frequent Flyer points to Singapore Airlines Krisflyer program.

The partnership is an opportunity so rare that SIA calls it

a world first for frequent flyers

The ratio is a relatively benign 1.35:1, with a minimum transfer of 5,000 plus a transfer fee; see the Terms and Conditions. But that does not get you very far to Airpoints either, as SQ KrisFlyer is also a dead-end program. KrisFlyer has more partners, but is also more restrictive than Velocity regarding expiration and redemption.