Application that is just what the peroxide blonde needs? (4,9)

'peroxide blonde needs?' is the definition.
The definition suggests a singular noun which matches the answer.

'application that is just what' is the wordplay.
I cannot really understand how this works, but
'application' could be 'treatment' (I have seen 'Application of remedy' mean 'treatment' so perhaps 'application' could also mean 'treatment') and 'treatment' is present in the answer.
'just' could be 'fair' (just can mean fair in the sense of showing justice) and 'fair' is present in the answer.
This accounts for all the letters.
This may be the basis of the clue (or it may be nonsense).

'the' is the link.

Can you help me to learn more?