What does a cistus plant look like or can you identifyThe plant in the photo?

Yep, looks like a Cistus to me

Agree, Cistus.

I wouldn't move it - its a lovely one. I wonder why you need to find a replacement? It may be tilting away from the wall/hedge behind it as cistus are sun lovers, but it looks very healthy. Many of them are lightly scented too - have you had a sniff?

Cistus corbariensis, one of the neatest and longest flowering. Masses of gleaming white fried eggs. They don't move well, because the roots are surprisingly sparse and sprawling, so the rootball doesn't hang together. Cistus generally aren't long lived. I would enjoy that one there, and find another for a new spot. Look up cistus x dansereaui (low habit, big white flower with dark blotch at the base of each petal), or C. pulverulentus 'Sunset' for a hot pink.

So disappointed to hear they aren't long lived - how long is long?