Quick to take shelter between foxtrot and tango (5)
I believe the answer is:
fleet
'quick' is the definition.
(I've seen this before)
'shelter between foxtrot and tango' is the wordplay.
'shelter' becomes 'lee' (as in lee side, the side sheltered from wind).
'between' is an insertion indicator.
'foxtrot' becomes 'f' (phonetic alphabet: alpha, bravo, charlie etc.).
'and' is a charade indicator (letters next to each other).
'tango' becomes 'T' (phonetic alphabet: alpha, bravo, charlie etc.).
'f'+'t'='ft'
'lee' going into 'ft' is 'FLEET'.
'to take' acts as a link.
(Other definitions for fleet that I've seen before include "Street of the hack" , "Fast moving" , "Fast - naval force" , "Navy - quick" , "Fast; London street, old prison" .)