Setup:
export VAR_ONE=thisIsVarOne
An alternative using an associative array:
$ unset newvar
$ declare -A newvar
$ newvar[${VAR_ONE}]="somePrefix${VAR_ONE}"
$ typeset -p newvar
declare -A newvar=([thisIsVarOne]="somePrefixthisIsVarOne" )
$ echo "${newvar[${VAR_ONE}]}"
somePrefixthisIsVarOne