Bear making Dee run off (6)
I believe the answer is:
endure
'bear' is the definition.
(both can mean to tolerate)
'dee run off' is the wordplay.
'off' is an anagram indicator.
'dee'+'run'='deerun'
'deerun' is an anagram of 'ENDURE'.
'making' acts as a link.
(Other definitions for endure that I've seen before include "Last or suffer patiently" , "Bear without giving up" , "Remain in existence; suffer" , "Last (anag.)" , "Bear, suffer" .)