Period that's long, endless (4)
I believe the answer is:
year
'period' is the definition.
(year is a kind of period)
'long endless' is the wordplay.
'long' becomes 'yearn' ('yearn' can be a synonym of 'long').
'endless' means to remove the last letter.
'yearn' with its last letter taken off is 'YEAR'.
'that's' is the link.
(Other definitions for year that I've seen before include "Complete cycle of seasons" , "One orbit round the sun" , "TV advert" , "Time taken by a planet to orbit the sun" , "Period of twelve months" .)