Puts away jug island woman's brought round (9)

'puts away' is the definition.
('imprison' can be a synonym of 'put away')

'jug island woman's brought round' is the wordplay.
'jug' becomes 'prison' (jug can informally mean a prison).
'island' becomes 'i'.
'woman' becomes 'ms' (Ms. is an example).
'brought round' means one lot of letters goes inside another.
'i'+'ms'='ims'
'prison' going into 'ims' is 'IMPRISONS'.