Carry on being strict on representative from the east (9)
I believe the answer is:
persevere
'carry on' is the definition.
(I've seen this before)
'strict on representative from the east' is the wordplay.
'strict' becomes 'severe' (I've seen this before).
'on' means one lot of letters go next to another.
'representative' becomes 'rep' (rep is a kind of representative).
'from the east' says the letters should be written in reverse (on a map from right to left).
'rep' reversed gives 'per'.
'severe' put after 'per' is 'PERSEVERE'.
'being' acts as a link.
(Other definitions for persevere that I've seen before include "Serve peer (anag.)" , "Persist, stick at" , "hold on" , "Continue regardless" , "Keep going" .)