Protester starts to experience regret after a month (7)
I believe the answer is:
marcher
'protester' is the definition.
'experience regret after a month' is the wordplay.
'experience regret' becomes 'er' (this might be a standard abbreviation which I don't know about).
'after' means one lot of letters go next to another.
'a month' becomes 'March' (March is an example).
'er' put after 'march' is 'MARCHER'.
'starts to' is the link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for marcher that I've seen before include "Frontiersman" , "Soldier on parade" , "who may be protesting?" , "Borderline" , "taking part in demonstration?" .)