Hi Carrie!

Introducing predatory insects is not necessary. We recommend pruning off the most damaged stem tips to reduce the aphid population. You can also spray the remaining with a strong spray from the hose to dislodge them. Local predatory insects, including the non-native, but effective lady beetle, will find them, if they haven't already. It is easier to spot adult lady beetles with their red shells than the larvae, which are likely present on your vine already! There are other beneficial insects that help control the aphid population as well, such as midges, parasitoid wasps, and syrphid flies. 

For the different life stages of lady beetles and how to recognize them, check out this guide. 
https://extensionentomology.tamu.edu/insect/lady-beetle/

Here is some more information from The Morton Arboretum on honeysuckle aphids: https://mortonarb.org/plant-and-protect/tree-plant-care/plant-care-resources/honeysuckle-aphid/#overview

Jamie