Let G be a transitive permutation group acting on a finite set Ω with | Ω | ⩾ 2 . An element of G is said to be a derangement if it has no fixed points on Ω, and by a theorem of Jordan from 1872, G contains such an element. In particular, by a theorem of Fein, Kantor and Schacher, G contains a derangement of prime power order. Nevertheless there exist groups in which there are no derangements of prime order, these groups are called elusive groups. Defining a natural extension of this we say G is almost elusive if it contains a unique conjugacy class of derangements of prime order. In recent work with Burness, we reduced the problem of determining the almost elusive quasiprimitive groups to the almost simple and 2-transitive affine cases. Additionally we classified the primitive almost elusive almost simple groups with socle an alternating group , a sporadic group or a group of Lie type with (twisted) Lie rank equal to 1. In this paper we complete the classification of the primitive almost elusive almost simple classical groups.