In a hurry, Harry, not having arrived in front of George (5)
I believe the answer is:
hying
'in a hurry' is the definition.
(I've seen this in another clue)
'harry not having arrived in front of george' is the wordplay.
'not having' indicates named letters should be taken away.
'arrived' becomes 'arr' (abbreviation used in transport).
'in front of george' becomes 'ing' (I can't justify this - if you can you should give a lot more credence to this answer).
'harry' with 'arr' taken away is 'hy'.
'hy'+'ing'='HYING'
(Other definitions for hying that I've seen before include "Going quickly" , "Moving fast" , "in a hurry" .)