American breaking into huge unknown religious building (9)
I believe the answer is:
monastery
'religious building' is the definition.
'american breaking into huge unknown' is the wordplay.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'breaking into' means one lot of letters goes inside another.
'huge' becomes 'monster' (I've seen this before**).
'unknown' becomes 'y' (algebra).
'a' going into 'monster' is 'monaster'.
'monaster'+'y'='MONASTERY'
(Other definitions for monastery that I've seen before include "Religious establishment" , "One vows to stay here" , "Community of monks" , "Where brothers gather" , "brother's house" .)