Explicit notice printed in rush, backing maker of... (7,8)

I believe the answer is:

graphic designer

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'of' is the definition.
I don't know anything about this answer so I cannot judge whether this works.

'explicit notice printed in rush backing maker' is the wordplay.
'explicit' becomes 'graphic' (similar in meaning).
'notice' becomes 'sign' (I've seen this in another clue).
'printed in' means one lot of letters goes inside another.
'rush backing maker' becomes 'deer' (I can't justify this - if you can you should believe this answer much more).
'sign' going within 'deer' is 'designer'.
'graphic'+'designer'='GRAPHIC DESIGNER'

Can you help me to learn more?

I've seen this clue in the Sydney Morning Herald.

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