Precede a problem with red tape (7)
I believe the answer is:
predate
'precede' is the definition.
(I know that precede can be written as predate)
'a problem with red tape' is the wordplay.
'a problem with' indicates an anagram.
'red'+'tape'='redtape'
'redtape' with letters rearranged gives 'PREDATE'.
(Other definitions for predate that I've seen before include "Track down and feed off" , "Go before" , "Be earlier in time" .)