Lodge or church more appropriate (7)
I believe the answer is:
chapter
'lodge' is the definition.
(chapter is a kind of lodge)
'church more appropriate' is the wordplay.
'church' becomes 'ch' (common abbreviation).
'more appropriate' becomes 'apter' ('apt' can be a synonym of 'appropriate').
'ch'+'apter'='CHAPTER'
'or' is the link.
(Other definitions for chapter that I've seen before include "Ecclesiastical assembly or subdivision of a written work" , "Episode" , "Sequence - section of book - church body" , "Division of written work" , "Division of book, usually numbered" .)