Short answer: Yes
Long answer:
In most of the case, you can.
I recently moved from Spark to Stuff-Fibre and I kept use the router from Spark. It worked. The only thing that I need to do is restarting the router. Nothing else.
I was worried about this as I asked Stuff-fibre not to send me the router and I didn’t know whether the privious one would work. Because the Spark router may be restricted to only work for Spark.
For the exactly same service, Spark charged me for $105, with the new company, on average, I pay $64 a month. I regret that I didn’t do this earlier. I couldn’t remember the previous speed. But the following speed is more than enough for me.
The router came with Spark is HG659b. It supports ADSL, VDSL and fibre. My previous plan with Spark was Fibre, I switch to Stuff-Fibre with the same level Fibre plan.
Note that I have to write to Stuff-fibre by email to cancel the route delivery, otherwise, I have to pay for the delivery fee. And the router is rent from them, I have to give it back after the 12 month contract. It seems there were some communication issue on their end. I still received a router, and they said that they will send me a prepaid post bag to ship it back. And my account is not charged for the delivery fee.
One problem with Stuff-Fibre is that I cannot find my home address in their system. Although I can manually enter my home address from they main page, but I prefer to use broadbandcompare website to buy the service, as I can get 3 months free rather than 2 months free. But this cannot be done as I cannot find my home address. I had to write to them before go further. Eventually, I did the process from their website with a wrong address (oh, I forgot to manually enter). Then they correct the promo code and address from their side.
It’s a great buy so far.