Brute taking side briefly, on reflection, might make them anxious (7)
I believe the answer is:
disturb
'make them anxious' is the definition.
I can't judge whether this definition defines the answer.
'brute taking side briefly on reflection' is the wordplay.
'brute' becomes 'brut' (I am not sure about this - if you are sure you should believe this answer much more).
'taking' means one lot of letters go next to another.
'briefly' means to remove the last letter.
'on reflection' says the letters should be written backwards.
'side' with its last letter taken off is 'sid'.
'brut'+'sid'='brutsid'
'brutsid' in reverse letter order is 'DISTURB'.
'might' acts as a link.
Can you help me to learn more?
(Other definitions for disturb that I've seen before include "Upset - agitate" , "Unsettle, discomfit" , "Make anxious" , "Agitate - ruffle - trouble" , "Ruffle - worry" .)