As the say goes, in order to have a chicken stew you need to have the chicken, well that is the same with Arbitrations, in order to start a claim through Arbitration, you need first to have an agreement to arbitrate, and such agreement to arbitrate has different ingredients that can be combined with each other in order to have a successful arbitration clause or agreement.
To this point, you have rightfully pointed out that the arbitration agreements can have the form of a clause within a contract or the arbitration agreement can take the form of an entire different contract, obviously relating to the main contract upon which you wish to settle possible legal problems.
One of the first elements, whether in the form of a clause or an agreement, you need to have an actual agreement, and such agreement must be clear as to the willingness of the parties to resolve their given disputes through arbitration.
The agreement must convey such “meeting of minds” to arbitrate, which implies as well an obligation and a right, the obligation means that the parties are obliged to bring their possible disputes before arbitration, and on the other side of the spectrum there is the right of the parties to have their dispute resolve before an Arbitral Tribunal.
At least draft something along these lines: “…the parties agree to have their current or future disputes to be resolved under arbitration…”
So, if there is an actual agreement to resolve the disputes under arbitration, then you at least are good to go.
However, you will need at least a second element, which is the “seat” of the Arbitral Tribunal, we will discuss later on the seat.