Stately bird - for example, one brought up in Dorset (7)

'in dorset' is the definition.
(swanage is in dorset)

'stately bird for example one brought up' is the wordplay.
'stately bird' becomes 'swan'.
'for example' becomes 'eg' ('e.g.' can be a synonym of 'for example').
'one' becomes 'a'.
'brought up' says the letters should be written backwards (down clues only).
'eg'+'a'='ega'
'ega' reversed gives 'age'.
'swan'+'age'='SWANAGE'