Dawdle around square at first under cold arcade (8)
I believe the answer is:
cloister
'arcade' is the definition.
(thesaurus)
'dawdle around square at first under cold' is the wordplay.
'dawdle' becomes 'loiter' (I've seen this before**).
'around' indicates putting letters inside.
'at first' indicates taking the first letters.
'under' means one lot of letters go next to another.
'cold' becomes 'c' (eg on taps).
The first letter of 'square' is 's'.
'loiter' enclosing 's' is 'loister'.
'loister' put after 'c' is 'CLOISTER'.
(Other definitions for cloister that I've seen before include "Covered passage round cathedral courtyard" , "Covered walk round quadrangle" , "Covered pillared arcade" , "Cathedral's covered walk" , "sacred enclosure?" .)