Operation controlled by thugs in suits from the outset ... and hats (5)
I believe the answer is:
topis
'hats' is the definition.
(topi is a kind of hat)
'operation controlled by thugs in suits from the outset' is the wordplay.
'operation' becomes 'op'.
'controlled by' indicates putting letters inside (some letters restrict or block in others).
'thugs in suits from the outset' becomes 'tis' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'op' put within 'tis' is 'TOPIS'.
'and' is the link.
Can you help me to learn more?
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