Dorothy's dog welcomes run about in provincial capital (7)
I believe the answer is:
toronto
'provincial capital' is the definition.
(capital of Ontario in Canada)
'dorothy's dog welcomes run about' is the wordplay.
'dorothy's dog' becomes 'toto' (Dorothy's dog in The Wizard of Oz).
'welcomes' is an insertion indicator (in sense of 'invites in').
'run' becomes 'r' (cricket abbreviation).
'about' becomes 'on' (as in a book 'on' a certain topic).
'r'+'on'='ron'
'toto' going around 'ron' is 'TORONTO'.
'in' acts as a link.
(Other definitions for toronto that I've seen before include "Canada's largest city" , "Big city" , "place on Lake Ontario" , "Transatlantic city" , "Ontarian capital" .)