Are becoming bothered primarily by police’s image (5)
I believe the answer is:
befit
'are becoming' is the definition.
(if something is becoming it suits or befits)
'bothered primarily by police's image' is the wordplay.
'primarily' indicates taking the first letters.
'by' says to put letters next to each other.
'police's image' becomes 'e-fit' (computer image of a suspect).
The initial letter of 'bothered' is 'b'.
'b'+'efit'='BEFIT'
(Other definitions for befit that I've seen before include "Become, suit" , "Be right and suitable for" , "Be appropriate for" .)