Mutual respect's beginning with police car going off (10)
I believe the answer is:
reciprocal
'mutual' is the definition.
('reciprocal' can be similar in meaning to 'mutual')
'respect's beginning with police car going off' is the wordplay.
'beginning' says to take the initial letters.
'with' means one lot of letters go next to another.
'going off' indicates an anagram.
The initial letter of 'respects' is 'r'.
'police'+'car'='policecar'
'policecar' with letters rearranged gives 'eciprocal'.
'r'+'eciprocal'='RECIPROCAL'
(Other definitions for reciprocal that I've seen before include "Mutual" , "Done in return" , "Cross" , "with give and take" .)