2 years in a pot is probably about its limit - needs to be put into the ground by now I expect. You could try a much, much larger pot, specially a deeper pot...

Permanent quarters for a climbing rose would be a minimum of a meter wide and deep, i. m. e. Otherwise, put it in the ground, if you can.

Yep..it would be happier in the ground as it gets quite big likes freedom to do it's own thing.

thanks for your answers everyone. Didn't realise that a large pot wouldnt be enough!Yes, will put it in the ground and do something else in the pot that climbs well.Any suggsestions on that? It's next to sturdy trellis and we already have two evergreen honeysuckles in that area so something different with lots of foliage would be good.The honey suckles are also in large pots but are doing ok.Its east facing but gets enough sun.

Yes! I have a lovely Zephirine rose by my front door. It's not the easiest rose to grow, but it got a second lease of life once it was moved from a pot to the ground and given lots of attention, and is currently showing how happy it is with a magnificent display of flowers - lovely to come home to!
I'm not very sure about a climbing replacement to go into the pot that is going to be happy there for any length of time. We have a lovely parthenocissus that gives a wonderful display of colour in autumn on the same north and the adjoining east wall, but that is both unsupported except by the wall itself, and I think it would be a bit fettered by the confines of even a large pot - although that may not be an entirely bad thing!

As you have evergreen honeysuckles there already, perhaps something that isn't evergreen would be okay? If so, and your pot is 2 feet deep by 12 inches wide, then consider a clematis hybrid, one of the smaller varieties such as Bees Jubilee, Nelly Moser, or for a late spring and summer flowering one, The President or Niobe. All these will do well in any aspect, so a morning's sun will be fine.