Go out for air by river — quarter's not suitable for everyone to see (7,5)

'go out' is the definition.
(to venture forth is to set out or go)

'air by river quarter's not suitable for everyone to see' is the wordplay.
'air by' becomes 'vent' (both can mean to express or reveal. I am not sure about the 'by' bit.).
'river' becomes 'ure' (river in Yorkshire).
'quarter' becomes 'fourth' (a quarter is a fourth of something).
'not' suggests deleting specific letters.
'suitable for everyone to see' becomes 'U' (Universal DVD certificate).
'fourth' with 'u' taken away is 'forth'.
'vent'+'ure'+'forth'='VENTURE FORTH'

'for' acts as a link.