No, not really. Conservationist as a term normally describes people who are interested in conservation, that is they want to promote and protect wildlife and the environment. I guess people who think it is important to preserve old buildings might also be called 'conservationists', but they are not the people who carry out the work. I think the term 'restorer' fits what you are looking for. https://en.wikipedia.org/wiki/Conservator-restorer I've not heard of the word 'conservator', but I do know the word 'restorer', and that's the word I would use.

I think they are called art restorers. Conservationists are members of the public who think it is important to preserve old historical buildings but they are not the people who do the restoration work.