Are you putting the new arch where the old one is now? You might be able to untangle the clematis you have now and lay it on the ground while you replace the arch. I've only tried moving a mature clem once but it died. If you are going to replace it then you might like a combination of a rose and a clematis? You can have fun deciding on colour combinations and whether you want the clem to flower before the rose or at the same time (Not all clematis flower in midsummer, and the pruning of the ones that flower in different seasons is different)
If you want to look at available roses try the David Austin site for some ideas.

Looking at the picture I would say that you have a Clematis montana, but hard to say without a close up picture of flower and leaves.

if you cant untangle the clem it can be cut down to about 3ft so you can then use it to climb up your new arch. [very nice too] you can get different clematis that flower at all times of the year [winter ones are often evergreen too] roses are also good but you might want to think of honeysuckle, winter jasmine etc. I have evergreen clems mixed in with the deciduous types.

Aww thank you all so much for answering my query:)
Yes the new Arch is going in the same place as the old one, at the end of my path just at entrance to back garden.
Roses would be lovely to go with a clematis as I love them but will probably end up like a pin cushion when I have to prune it :) I'll definitely look at the David A site .
I just googled the Montana and it DOES look like it could be that Myron !
Thanks seaburngirl , I love my new Arch. Just been chatting to him indoors and he thinks we should start with new plants as the present one is planted a couple of foot away and seems to be stretched or pulled towards the arch.
I'm off now to look up all the flowers you've all suggested. Thanks :) x

Rosa 'Leverkeusen' is a good one, pale yellow, suitable for an arch, and tough as old boots. It has a main flowering time in the summer, and some more later in the season as well

Ooh that sounds ideal Andrew. Off to google that one :)

Zepherine Drouhine is a thornless climbing rose that may suit

I have Zepherine Drouhine and Climbing Iceberg either side of my arch with clematis too. then on a wall trellis I have New Dawn with clematis Victoria growing through it. There are some wonderful climbers from really tiny flowers to larger ones. Just remember that catalogue images are often 'touched up' to enhance the colours. I have been caught out that way many years ago.

I looked these all up and have decided on the zephirine drouhin and a couple of different clematis for my Arch. I'm going to say goodbye to the old clematis that's already there as its very old and gnarled now .
I love the honeysuckle so think I would like one somewhere in my garden :)
Snoopdog I, looking forward to learning things too as I was in a flat before we bought this house :)