We introduce the conditional $p$-dispersion problem (c-pDP), an incremental variant of the $p$-dispersion problem (pDP). In the c-pDP, one is given a set $N$ of $n$ points, a symmetric dissimilarity matrix $D$ of dimensions $n\times n$, an integer $p\geq 1$ and a set $Q\subseteq N$ of cardinality $q\geq 1$. The objective is to select a set $P\subset N\setminus Q$ of cardinality $p$ that maximizes the minimal dissimilarity between every pair of selected vertices, i.e., $z(P\cup Q) ≔ \min\{D(i, j), i, j\in P\cup Q\}$. The set $Q$ may model a predefined subset of preferences or hard location constraints in incremental network design. We adapt the state-of-the-art algorithm for the pDP to the c-pDP and include ad-hoc acceleration mechanisms designed to take advantage of the information provided by the set $Q$. We perform exhaustive computational experiments and show that the proposed acceleration mechanisms help reduce the total computational time by a large margin. We also assess the scalability of the algorithm and derive managerial insights regarding the value of building a network from scratch compared to an incremental design.