Arrive and, reversing, put the runabout inside (4,2)

I believe the answer is:

turn up

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'arrive' is the definition.
(thesaurus)

'reversing put the runabout inside' is the wordplay.
'reversing' is a reversal indicator.
'the runabout' becomes 'urn' (I can't justify this - if you can you should believe this answer much more).
'inside' means one lot of letters goes inside another.
'put' backwards is 'tup'.
'tup' placed around 'urn' is 'TURN-UP'.

'and' is the link.

Can you help me to learn more?

(Other definitions for turn up that I've seen before include "Increase strength" , "part of leg" , "make louder" , "Appear by chance - increase volume" , "put in an appearance" .)

I've seen this clue in the Evening Standard.

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