Close - doubly close in fact (6)
I believe the answer is:
nearby
'close doubly close in fact' is the definition.
'nearby' can be an answer for 'close' (I've seen this before). I am not sure about the 'doubly close in fact' bit.
'close doubly close' is the wordplay.
'close doubly' becomes 'near' (similar in meaning. I am not sure about the 'doubly' bit.).
'close' becomes 'by' (I've seen this in other clues).
'near'+'by'='NEARBY'
Can you help me to learn more?
(Other definitions for nearby that I've seen before include "Close at hand, not far away" , "Around the corner" , "Adjacent" , "Barney (anag)" , "A short distance away" .)