The form of contract that will be used for this agreement depends on the type and size of the project. In the case of a major developer acting as a client, there might be a contract that has already been prepared by the client and each consultant/sub-consultant will need to sign it before getting on board with the rest of the design team. The terms and conditions of such a contract are then set by the client and the consultant is in a disadvantageous position.
With repeated work from a trusted client involving small scale projects, there’s usually an exchange of letters between the client and the consultant, confirming the consultant’s appointment for a new job. This often works on the basis of the terms and conditions of the agreement to have been formally exchanged at some point early in the relationship but having been left aside on the basis of trust building between the two and a good working relationship.
It’s still however best practice to always have a thorough written agreement before committing to an appointment, since the relationship could fall out and financial matters can be hard to resolve without robust written evidence.