Old wood is wood that was formed in previous years; it's the brownish hard stuff. New wood is, well, new - it's what has grown during this growing season, and is, at this point, soft and almost certainly green. This year's new wood is next year's old wood.

I have a native wisteria, which I cut back as needed after it blooms. Pay attention to yours this year, and figure out if it's on old or new wood, and then you'll be set for the future.

Do you know what kind of wisteria you have - Chinese, Japanese, or native...? Japanese and Chinese both bloom on 'old' wood; the native ones bloom on 'new' wood. I have both Chinese and Japanese (grown as 'trees'/'shrubs') but not a native one, so I don't know a lot about how those ones develop. But, since they flower on 'new' wood and yours hasn't flowered, I'm guessing it's either Japanese or Chinese. Pruning is certainly the way to promote flowering in my experience. It can indeed be an almost weekly chore at times! Both my wisterias did their first spring flowering at 5 years in the ground. The Chinese ones tend to do a secondary summer bloom if you keep them pruned, and my Chinese one started putting out summer blooms in its second year, but took 5 years to do a spring flowering. The Japanese ones are less inclined to do a secondary summer bloom so it took five years before we saw the first flowers. But I knew it was going to flower eventually because it started putting out flowering spurs by its second year. While it flowers along the stems too, the presence of short, stubby spurs signals that it is maturing towards the flowering state. The spurs look like this:

Chinese wisteria blooms before most of the leaves appear while Japanese ones bloom after the leaves have emerged. The new leaves on Chinese ones are bronzy while the Japanese ones leaves emerge green. My guess is that you have a Japanese one - so it could still flower yet this spring - check under those leaves for buds....

If it doesn't flower this year, wait until the leaves drop this fall and assess whether it has developed the spurs. If it has, have patience; it will bloom... If there are no spurs, it's probably not worth keeping.

First flowers on my Japanese one last spring:
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I've got my fingers crossed for a bigger show this spring....

I cannot remember where this wisteria came from. I may have dug it up from the woods around my Mothers house years ago. I'm going to try to prune it again and hold out for another year but the growth in the picture is from the past two weeks. Its a monster grower. I'm not sure I can devote the time to pruning it all summer again...

Spring is certainly a time of vigorous growth for them. It usually slacks off a bit in summer but pruning is a steady chore. If you're not prepared to do the necessary pruning to keep it in control, then you're better off to remove it.