Here is another picture of the full plant.

I would definitely cut it back and try to re-pot the cuttings but not necessarily in the same pot. Once you cut it back it should start a lot of new growth. Continue to cut back everything that reaches a certain length and it should thicken up.

Also, you may want to check for mites, I always get those little butters in my ivy and they do a lot of damage.

As well, once its warm enough outside move it out there and you should see a big increase in growth.

Goodluck,
Tuck

i would cut back. inspect for spider mites, they are a major nuisance with this plant

I think it looks fantastic! Vines don't usually branch out much unless encouraged to do so by cutting the existing tips. They are in search of something to climb.

Maybe you could put another upright plant in the pot also, to achieve a fuller look.

Tendrils are curly little things that grow along the stems of some vines and wrap around anything they can grab. Ivy has aerial roots instead of tendrils. The pieces of the vine are called shoots or stems, or just vines.

i have the same type of ivy. but i only keep it indoors over winter. and it gets very ratty by april and drops most of its leaves: mostly from mites damage. it looks now very similar to yours.i shower it and mist it and lay systemic insectiside on it , it just barely survives. once i put it outside - it completely recovers and gets very bushy. it likes being cool and moist, not hot and dry. one year i had extreme mite damage + it dried up in the western window when i was away - had just long branches left. but it completely regrew and recovered outside come spring/summer. it really needs to be outside. it's not an indoor plant. it is not very easy to root it from cuttings either - best to do it during summer.