Restoring brittle/dry canvas webbing?

[Captain Croft]

Hi all, 

 

I recently bought a lovely vintage map case for use as a private purchase for my officer kit (it may not actually be period). The canvas is very dry and I’m a little worried it might not stand up to much if worn at the belt. It’s only for gentle walking around, not battle re-enactment but I’d like to do my best to get it as supple and strong as possible.

 

any suggestions? Images attached (note the strap is actually my spare haversack strap).