I can't see the foliage - can you supply some images of that? However, I suspect this is Muehlenbeckia australis (pohuehue) which is indigenous and semi-deciduous. It likes disturbed areas and can at times be a aggressive 'weedy' plant in urban situations. It often forms hybrids with tororaro (M. complexa) which can compound the 'weedy' nature.
Sorry I cannot advise on its control - beyond suggesting you hand pull it, or tolerate it as it attracts native butterflies (coppers especially) and lizards.