Archeopteryx is a connecting link between reptiles and birds but is not a living fossil. ( it is extinct)
Rhynia is a connecting link between bryophytes and pteridophytes and that too, is not a living fossil. ( it is extinct)
Now other living organisms which are connecting links but are not living fossils:
Chimaera ( a fish) is connecting link between bony and cartilagenous fishes ( and is living but not a living fossil)
Cycas is a connecting link between pteridophytes and Gymnosperms ( and is living but not a living fossil )
Please feel free to ask any follow up question and approve the answer if you think it’s useful :)