The narrow part is worth saving (4)
I believe the answer is:
neck
'the narrow part' is the definition.
(I've seen this before)
I cannot understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for neck that I've seen before include "Narrow connecting part - smooch" , "part of instrument such as guitar" , "Narrow part of e.g. isthmus" , "jowl?" , "Adam's apple location" .)