Quickly look in both directions (4)
I believe the answer is:
peep
'quickly look' is the definition.
'peep' can be an answer for 'look' (peep can mean to look at something). I am not certain of the 'quickly' bit.
'in both directions' is the wordplay.
'in' is an insertion indicator.
'both' becomes 'pp' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'directions' becomes 'ee' (the abbreviation for east written twice).
'pp' going around 'ee' is 'PEEP'.
Can you help me to learn more?
(Other definitions for peep that I've seen before include "Look surreptitiously - through a keyhole?" , "Palindromic glimpse" , "Spy" , "Look quickly" , "Look surreptitiously, like Tom" .)
