Same goes for project managers!

* always show respect towards all parties

* the first consultant must have done something right, otherwise (s)he wouldn have been the first consultant. So give honour where honour is due.

* on the other hand the first consultant must have done something wrong, otherwise (s)he wouldn be replaced.
So try to get on speaking terms with the first consultant for usefull advise. Forewarned is forearmed, usually there are more sides to the situation.
But also listen carefully to the views of the client, (s)he will decide *your* success and will sign off on your time sheet.