Note their problem and hesitate (6)
I believe the answer is:
dither
'hesitate' is the definition.
(I've seen this before)
'note their problem' is the wordplay.
'note' becomes 'd' (musical note).
'problem' is an anagram indicator.
'their' with letters rearranged gives 'ither'.
'd'+'ither'='DITHER'
'and' acts as a link.
(Other definitions for dither that I've seen before include "Waver, be indecisive" , "'Vacillate, hesitate (6)'" , "Be indecisive, hesitate" , "Hit red in order to vacillate" , "Shilly-shally" .)