Given cover is under construction (7)
I believe the answer is:
insured
'given cover' is the definition.
The definition and answer can be both related to thinking as well as being past participle verbs.
Maybe you can see an association between them that I can't see?
'is under construction' is the wordplay.
'construction' is an anagram indicator (answer constructed from certain letters).
'is'+'under'='isunder'
'isunder' anagrammed gives 'INSURED'.
Can you help me to learn more?
(Other definitions for insured that I've seen before include "Financially protected" , "Covered against mishaps" , "Covered for losses" , "Covered for loss" , "Protected against risk" .)