Second sign of hesitation to enter filthy house (9)
I believe the answer is:
monastery
'house' is the definition.
(monastery is a kind of house)
'second sign of hesitation to enter filthy' is the wordplay.
'second' becomes 'mo' (both are short periods of time).
'sign of hesitation' becomes 'er'.
'to enter' is an insertion indicator.
'filthy' becomes 'nasty' (synonyms).
'er' placed within 'nasty' is 'nastery'.
'mo'+'nastery'='MONASTERY'
(Other definitions for monastery that I've seen before include "Where brothers gather" , "Religious establishment" , "Religious house" , "One vows to stay here" , "brother's house" .)