Secular state maintained by University with permission (10)

'secular' is the definition.
(not blessed or hallowed)

'state maintained by university with permission' is the wordplay.
'state' becomes 'NH' (abbreviation for the US state New Hampshire).
'maintained by' means one lot of letters goes inside another (maintain can mean to keep hold of).
'university' becomes 'u' (abbreviation for university).
'with permission' becomes 'allowed' (allowed to do something).
'u'+'allowed'='uallowed'
'nh' placed into 'uallowed' is 'UNHALLOWED'.