Shut up at the inside: that's clear (6)
I believe the answer is:
patent
'clear' is the definition.
(synonyms)
'shut up at the inside' is the wordplay.
'shut up' becomes 'pent' (synonyms).
'the inside' is an insertion indicator.
'pent' placed around 'at' is 'PATENT'.
'that's' is the link.
(Other definitions for patent that I've seen before include "plain" , "Obvious - property right to invention" , "This leather has a glossy varnished surface" , "Obvious - protection for inventors" , "Like a medicine" .)