No. Unless specifically agreed in writing, you will not be entering into an exclusive relationship with Third Bridge.
The only instance in which Third Bridge does impose a restriction is if Third Bridge introduces you to a client for the first time. If this is the case, you should not contact the client directly and should go through Third Bridge for a period of one year following your last consultation with the client.
The intention is to prevent consultations from taking place which bypass Third Bridge, where Third Bridge has made the introduction to the client.