bash loop with jq [closed]

Could be something like:

set -o pipefail
while
  token=$(jq -e .queryToken Process.json) &&

    curl --insecure \
         --fail \
         --no-progress-meter \
         --location \
         --user "uname:pswd" \
         --data "$token" \
         'https://api.../queryMore' |
      jq -c --slurpfile old Process.json '
        . as $new |
        $old | first |
        .numberOfResults += ($new.numberOfResults) |
        .result += ($new.result) |
        .queryToken = ($new.queryToken)' > Process.json.new &&

    mv Process.json.new Process.json
do
  continue
done

(also replacing your -k with its long form --insecure so as not to loose sight of the fact that it is insecure. Also adding --fail for curl to report errors by the HTTP server; I've also moved the URL to the end. Having it after --location was misleading, as it's not an argument to that option; --location is a flag to tell curl to follow redirects¹; you should also consider using safer ways to pass the credentials as passing them on the command line is insecure).

^{¹ as supplied by the HTTP server in the Location HTTP header. See also the --location-trusted for the --user credentials to also be sent to the target of the redirection (potentially dangerous especially when combined with -k aka --insecure).}