Restraint on anaesthetic at the treatment centre (6)
I believe the answer is:
tether
'restraint' is the definition.
(tether is a kind of restraint)
'anaesthetic at the treatment centre' is the wordplay.
'anaesthetic' becomes 'ether' (ether is a kind of anaesthetic).
'at' means one lot of letters go next to another (I've seen this in other clues).
'centre' indicates the central letters.
The central letter of 'treatment' is 't'.
'ether' put after 't' is 'TETHER'.
'on' acts as a link.
(Other definitions for tether that I've seen before include "Rope to hobble a horse" , "Restrictive rope fixed to one spot" , "Tie up with a rope, an animal perhaps" , "Restrain within limits" , "Rope restricting animal's movement" .)