Took cover without hesitation, being close (5)
I believe the answer is:
humid
'close' is the definition.
(I've seen this before)
'took cover without hesitation' is the wordplay.
'took cover' becomes 'hid' (I've seen this before).
'without' means one lot of letters goes inside another ('without' can be similar in meaning to 'outside').
'hesitation' becomes 'um' (um is said in hesitation).
'hid' placed around 'um' is 'HUMID'.
'being' acts as a link.
(Other definitions for humid that I've seen before include "Damp, steamy" , "Rather wet" , "'Moist, damp (5)'" , "Warm and steamy" , "sticky" .)