Try moving east? Go quickly! (4)

I believe the answer is:

hare

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'go quickly' is the definition.
(hare can mean to run fast)

'try moving east?' is the wordplay.
'try moving' becomes 'har' (I can't justify this - if you can you should give a lot more credence to this answer).
'east?' becomes 'E' (abbreviation).
'har'+'e'='HARE'

Can you help me to learn more?

(Other definitions for hare that I've seen before include "Rabbit-like animal" , "'Swift, long-eared animal (4)'" , "Leveret" , "Long-eared mammal" , "Mammal like a large rabbit" .)

I've seen this clue in The Times.

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