After mine blooms on early June, I remove all the spent blooms. Given the number of flowers on it this takes a bit of time but mine is now blooming again.
Yes, deadhead it for a better repeat.

There is a theory that due to overpropagation New Dawn is starting to revert to its parent the once blooming Dr Van Fleet. I don't know how true this is, but a lot of people get a beautiful September rebloom while other people get nothing after June. Our New Dawn blooms throughout the season with deligent deadheading.

I've heard that it needs to be deadheaded but not cut back severely. Otherwise it spends a lot of time regrowing cane--unless this is what you want.

If you didn't remove the spent blooms in June, ND will have set a lot of hips (fruit). Letting these develop causes a great reduction in repeat bloom. With a climber, you don't have to be fussy about how you deadhead-- just use the hedge trimmers and whack off most of the blooms and fruit. Cut the lateral shoots (blooming spurs) back to 2 or 3 leaves, but let the long basal shoots develop without interruption.

However, if your plant is 6 years old and has not repeated at all, it may have been cloned from a stem that had mutated back to the once-blooming form named Dr. Van Fleet. There is nothing to be done about that except to replace the plant. However, Dr. Van Fleet is still worth growing.

I grew two NDs for many years over an arbor that spanned my double french doors. While it had a glorious spring bloom, there was sparse rebloom. It spent most of the summer and fall growing long, long canes that would reach the second story bedroom window. My DH would sometimes open the window and prune them instead of getting out the ladder. They were so tall and thick that birds would make their spring nests in them.
-terry

The only time I got any rebloom off of mine was when I pruned it quite a bit after it bloomed in June/July. It rebloomed quite late in the season, actually well into the fall and some of the blooms got zapped by heavy frost. But it was an unexpected treat to have ND in heavy bloom in Oct.