Predominantly with some dampness but no current (6)
I believe the answer is:
mostly
'predominantly' is the definition.
(thesaurus)
'with some dampness but no current' is the wordplay.
'with some dampness' becomes 'moistly'.
'but no' is a deletion indicator.
'current' becomes 'i' (symbol for electric current).
'moistly' with 'i' removed is 'MOSTLY'.
(Other definitions for mostly that I've seen before include "Largely" , "For the greater part; usually" , "In the main, nearly all" , "On the whole" , "More often than not" .)