If you contact Ekornes and give them the details from the label underneath the items (or at least one of them) then it is very possible they can supply the leather covers/overalls complete. After that you could contact a local Ekornes dealer who may just do the changeover for you. Alternatively Ekornes may be able to advise where to go. This will of course not be cheap and you may wish to replace yours completely, especially if it is decades old. If the relatively new leather was ruined by a pet then that is another story - I once saw a full three piece set which had been cat clawed to bits.
For those who did not take to the chairs, it is important to have the correct size of chair, each model comes in three sizes, I think. If the size is wrong for you, the chair will not be nearly as good in use as one that actually fits. People are inclined to buy them on a similar basis to "classic" furniture and thus end up with too big a chair, even far too big. Those who like to slump in chairs will not like the postured position. Those suffering from a bad back (often as not from slumping) can develop pain free posture habits aided by good chairs. We have had Stressless furniture for something like 25 years and, if we had to buy new, we would not have anything else.