Husband gags terribly, swallowing one delicacy (6)
I believe the answer is:
haggis
'delicacy' is the definition.
(I have seen 'Scottish delicacy ' mean 'haggis' so perhaps 'delicacy' could also mean 'haggis')
'husband gags terribly swallowing one' is the wordplay.
'husband' becomes 'h' (abbreviation).
'terribly' indicates anagramming the letters.
'swallowing' is an insertion indicator.
'one' becomes 'i' (Roman numeral).
'gags' with letters rearranged gives 'aggs'.
'aggs' enclosing 'i' is 'aggis'.
'h'+'aggis'='HAGGIS'
(Other definitions for haggis that I've seen before include "Scottish offal dish" , "Indonesian island; computer language" , "Robert Burns' "Great chieftain o' the puddin'-race"" , "Scotish sheep dish" , "Burns' night dish" .)