Defunct deity with a straight face (7)
I believe the answer is:
deadpan
'a straight face' is the definition.
(thesaurus)
'defunct deity' is the wordplay.
'defunct' becomes 'dead' ('dead' can be similar in meaning to 'defunct').
'deity' becomes 'pan' (Pan is an example).
'dead'+'pan'='DEADPAN'
'with' is the link.
(Other definitions for deadpan that I've seen before include "Serious-looking" , "with emotionless face" , "With expressionless face" , "Blank" , "Keeping a straight face" .)