Professional US magazine, highly esteemed, grew rapidly (12)

I believe the answer is:

proliferated

'grew rapidly' is the definition.
('proliferate' can be a synonym of 'grow rapidly')

'professional us magazine highly esteemed' is the wordplay.
'professional' becomes 'pro' ('pro' can be a synonym of 'professional').
'us magazine' becomes 'life'.
'highly esteemed' becomes 'rated'.
'pro'+'life'+'rated'='PROLIFERATED'

I've seen this clue in The Telegraph.

Want a hint initially instead of a full solution? Install my app