You could re-enter the country as a visitor, but you are not allowed to work at all on a visitor's visa.
If you are British, you could look at the possibility of going for a BUNAC IEP visa
http://www.bunac.org/uk/work-abroad/...-zealand/visas, which you can have even if you've already used the WHV option.
Otherwise, and after you've had that, you can only get a work visa if you have a skill and can meet the requirements for one of the work visas
http://www.immigration.govt.nz/migrant/stream/work/, or else, if you have a partner who is a NZ citizen, resident, or work visa holder, you can apply to be partner-sponsored for a temporary work visa when you can show proof of having lived with your partner for around three months.
http://www.immigration.govt.nz/migra...milystream.htm This last visa is an open visa which allows you to take any job offered, without its needing to be skilled.