Built before beginning of century, and oddly trendy (7)
I believe the answer is:
erected
'built' is the definition.
(erecting is a kind of building)
'before beginning of century and oddly trendy' is the wordplay.
'before' becomes 'ere' (poetic term for 'before').
'beginning of' suggests taking the first letters.
'and' says to put letters next to each other.
'oddly' indicates alternate letters (letters in the odd-numbered positions are used).
The first letter of 'century' is 'c'.
The alternate letters of 'trendy' are 'ted'.
'ere'+'c'+'ted'='ERECTED'
(Other definitions for erected that I've seen before include "Fixed up" , "Put up (a building)" , "No Clue" , "Constructed, built" , "Set up" .)