If you haven’t got the space/means to train the stems then you’d be better off replacing it with a shrub rose.
If you can install some wires along a fence, then wait until late Feb/early March to cut back (fairly rigorously) and then start training the main stems on the supports - check out the David Austin website, lots of great care info and videos.
But, again, if you have no means of doing this then it’s best to say goodbye to the climber (which has nothing to climb!) and replace with either a shrub rose or a standard (tree) rose.
If you do decide to replace it, Id dig it out mid-autumn (if you’re still getting flowers, might as well enjoy them for now). Dig out as much of the root system as possible. Also, remove a good foot of soil - refill with a good mix of well-rotted manure and new top soil mixed together. Then, next year, choose and plant your new shrub/tree rose. If possible, also add some granular fungi to the hi,e you dig for your new rose (again, check out the David Austin site for this). It aids good root development.
David Austin site also details a handy calendar of what to do, and when, throughout the year. I learnt a lot from that (including that I’d probably been overwatering).
Roses can make an amazing garden, but there’s no point having one if the conditions for it aren’t possible (ie a climber that has nowhere to climb or be trained to climb).