Intruder tied up by person unknown (8)
I believe the answer is:
busybody
'intruder' is the definition.
(thesaurus)
'tied up by person unknown' is the wordplay.
'tied up' becomes 'busy' (similar in meaning).
'by' means one lot of letters go next to another.
'person' becomes 'bod' (bod can informally mean a person or body).
'unknown' becomes 'y' (algebra).
'busy'+'bod'+'y'='BUSYBODY'
(Other definitions for busybody that I've seen before include "One minds everyone else's business" , "Person who meddles in the affairs of others" , "Meddlesome type" , "he'll nose around" , "butter in" .)