Their problem - time and tradition (8)
I believe the answer is:
heritage
'tradition' is the definition.
(I've seen this before)
'their problem time' is the wordplay.
'problem' is an anagram indicator.
'time' becomes 'age' (an age is a period of time).
'their' is an anagram of 'herit'.
'herit'+'age'='HERITAGE'
'and' acts as a link.
(Other definitions for heritage that I've seen before include "Objects and cultural traditions passed down" , "Our historic legacy" , "That which is passed down by tradition" , "Received culture and background" , "Valued survivals from the past" .)