It does away with the need for screws! (7,5)
I believe the answer is:
private means
'the need for screws' is the definition.
I don't know anything about this answer so I cannot judge whether it can be defined by this definition.
'it does away' is the wordplay.
I cannot quite understand how this works, but
'it' could be 't' (abbreviation. e.g. in 'tis) and 't' is found within the answer.
'away' could be 'a' (abbreviation as used in sports fixtures) and 'a' is found in the answer.
This may be the basis of the clue (or it may be nonsense).
'with' is the link.
Can you help me to learn more?
(Other definitions for private means that I've seen before include "Income other than salary" , "make money from investments" , "source of income" , "Unearned income" .)