The arbitration clause, in Italian jurisdiction as well as in a number of other jurisdictions, does not constitute an ancillary clause of the underlying contract. On the contrary, it constitutes a separate contract with procedural effects. This principle is usually referred to as separability doctrine.
Under Italian law, this doctrine, based on Article 808 of the Italian Code of Civil Procedure (whereby "The validity of the arbitration clause must be evaluated independently of the underlying contract"), is only derogated in bankruptcy matters (under Article 83-bis of Italian bankruptcy law: I have examined the issue in this post).
This doctrine must also be taken into account if an agreement to agree (which is valid and enforceable under Italian law, and it is quite common in construction and conveyancing) is entered into, containing an arbitration clause, and the subsequent agreement does not contain the arbitration clause. I have already examined this topic a few years ago (in this post). Nonetheless, in the light of its relevance, also from a practical point of view, I consider that it is appropriate to examine it again. The opportunity to do so is offered by a recent decision issued by the Court of Appeal of Brescia (decision No. 1474 of 10 October 2019, Italian text available here).