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 tell whether this works.
'it does away' is the wordplay.
I cannot quite see how this works, but
'it' could be 't' (abbreviation. e.g. in 'tis) and 't' is found in the answer.
'away' could be 'a' (abbreviation as used in sports fixtures) and 'a' is found within the answer.
This may be the basis of the clue (or it may be nonsense).
'with' acts as a 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" .)