Company president going after trade with road authority! (7,3)

I believe the answer is:

traffic cop

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'road authority' is the definition.
The answer and definition can be both people as well as being singular nouns.
Perhaps they are linked in a way I don't understand?

'company president going after trade' is the wordplay.
'company' becomes 'co' (abbreviation).
'president' becomes 'p' (common abbreviation eg in VP).
'going after' means one lot of letters go next to another.
'trade' becomes 'traffic' (trafficking is a kind of trading).
'co'+'p'='cop'
'cop' put after 'traffic' is 'TRAFFIC COP'.

'with' acts as a link.

Can you help me to learn more?

I've seen this clue in The Guardian.

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