Make agreat tea ut of the hips... tastes pretty good and loaded with Vitamin C. However, you really don't have to deadhead this type of rose. Most "climbing roses" (they don't really vine type "climb") only bloom once perseason and the purpose for deadheading any flower is to encourage re-blooming... won't work with climbers... Secondly, leaving the bright yellow hips will feed some birds in the winter...
Having said all that... you may wish to "train" the rose by selectively pruning it after it goes dormant. My guess is the flowers on your rose are 4 or 5 petals which makes it a "wild rose" derivative. Very hardy and will cover a bare wall very well if pruned and tied up where you want it to go.
By the way, the Vitamin C in the hips degrades fairly quickly... best to keep it in a plastic bag in the fridge and then only fora fewweeks at most...