IRule for URL redirect

You can use the getfield option to extract that objectid, something like, if there are multiple other hosts coming to this setup, you can add host condition and then take action too.

ltm rule objectid_redirect {
when HTTP_REQUEST {
set uri [HTTP::uri]
set id [getfield $uri "/" 5]
log local0. "ObjectID is $id"
HTTP::redirect https://redirect.mytest.com/api/LinkServ?objectID=$id
}
}

Hope it helps. Test & update us.