Rich person’s factory, one on Yorkshire river (11)
I believe the answer is:
millionaire
'rich person's' is the definition.
('millionaire' can be a synonym of 'rich person')
'factory one on yorkshire river' is the wordplay.
'factory' becomes 'mill' ('mill' can be a synonym of 'factory').
'one' becomes 'i' (Roman numeral).
'yorkshire river' becomes 'aire' (I've seen this before).
'mill'+'i'+'on'+'aire'='MILLIONAIRE'
(Other definitions for millionaire that I've seen before include "See 14" , "Very wealthy person" , "Rich fellow" , "Airline limo (anag) - rich person" .)