Thus hair holds up prisons (4-3)

'thus hair' is the definition.
I know nothing about this answer so I can't tell whether this works.

'holds up prisons' is the wordplay.
I cannot really understand how this works, but
'up' is present in the answer.
'holds' could be 'locks' (lock is a kind of hold) and 'locks' is located in the remaining letters.
No letters remain.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?