It's hard. First, you've got the new teak - older teak has finer grain and is usually evenly colored. Teak these days seems to be coarser grained and has light and dark striations. Not a bad look but doesn't look like the old stuff.
Next, you've got the color. Most of the time, teak has not been stained. Just finished with varnish or polyurethane. Then it has aged. And the color changes.
Third, you've got the sheen. Gloss finish is usually fairly easy. It's glossy - unless it's badly worn. Then you need to stick a coat on the old as well as the new.
However, if you've got a satin finish, there are many degrees of satin - ranging from very flat to almost glossy. Tough to match unless, like the worn gloss, you finish the old to match the new.
One word: Curtains.