Pine cut short for a period of time (4)
I believe the answer is:
year
'a period of time' is the definition.
(year is a kind of period of time)
'pine cut short' is the wordplay.
'pine' becomes 'yearn' (synonyms).
'cut short' means to remove the last letter.
'yearn' with its last letter taken away is 'YEAR'.
'for' is the link.
(Other definitions for year that I've seen before include "Pupil group" , "See 9" , "365 or 366 days" , "Jan to Dec" , "One tenth of a decade" .)