To finish a story for the listeners takes ages! (5)
I believe the answer is:
years
'ages' is the definition.
(I've seen this in another clue)
'to finish a story for the listeners' is the wordplay.
'to finish' says to take the final letters.
'for' means one lot of letters go next to another.
'the listeners' becomes 'ears' (body parts which listen).
The final letter of 'story' is 'y'.
'y'+'ears'='YEARS'
'takes' is the link.
(Other definitions for years that I've seen before include "12 month periods" , "Ages" , "Units of time" , "Age" , "Long periods" .)