Tightens up on prison staff (6)
I believe the answer is:
screws
'tightens' is the definition.
(screwing is a kind of tightening)
'up on prison staff' is the wordplay.
I cannot quite understand how this works, but
'on' could be 're' ('on' can be mean 'with reference to') and 're' is found within the answer.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for screws that I've seen before include "Fastner with spiral thread" , "Prison warders (sl.)" , "... men guarding prisoners" , "Grooved fastening devices" , "Fix in place (6)" .)