Exemplar causes (also sometimes known traditionally as ideas* or original forms) are commonly defined in various ways -- as forms such that effects imitate them out of the intention of agents determining their own ends, as pre-existing substantifying reasons of existing things, as that which an artisan regards in effecting what he determines to be, as that which is the standard of truth and propriety for what is made, as that to which an effect is assimilated and conformed. It is an important kind of cause, and it is not difficult to find cases of it. For instance, in building something one may follow a blueprint; a novelist writes the actual version of the novel he has pre-thought; a teacher may set a standard example that is imitated by students. But what kind of cause is it?
The standard Aristotelian view, of course, is that there four proper causes: efficient (in Aristotle himself the somewhat narrower motive cause), material, formal, final. There are good reasons to think that the exemplar cause is not any of these. It is very obviously not a material cause. It also cannot be a formal cause, because both matter and form are intrinsic or constituent causes, and the exemplar is very definitely separate from the exemplate that derives from it. Thus one might try to make it out to be an efficient cause or a final cause, but in fact the exemplar cause does not have the same relation to the exemplate that the efficient has to the effect or that the final cause has to that which tends to it.
One might hold, then, that it is a fifth cause, and in practice it is often treated as such. However, there is good reason to think that there are exactly four proper causes. In addition, while it can't be an efficient, formal, or final cause, the exemplar cause is suspiciously similar to all three. Indeed, we see this in some of its descriptions: the exemplar is the form which the effects imitate from the intention of agents determining their own ends.
The four proper causes are those to which all causes can be traced back. But there are many other kinds of causes. There is nothing that requires us to say that every kind of causation traces back to only one kind of proper cause, as if these were summa genera of causation. Other causes can arise from the various ways these four interact in the real world. Their causation will, in principle, be explicable in terms of the four proper causes, but this may be quite complex, and it does not mean that the derivative causes are not causes in their own right, only that they are not the most basic building-blocks of causation. When they are causes in their own right, rather than just causal systems, they will have an overall action like that of one of the proper causes (because they will be organized by a particular relationship to a result), but this will arise from the interaction of various proper causes.
Perhaps the most popular, and I think, correct, view of exemplar causes is that they are extrinsic formal causes. Exemplar causes, as I said, cannot be proper formal causes because exemplars are not intrinsic forms. Nonetheless, they function a lot like formal causes. The reason this is possible is that the final cause, as cause of causes, can make it so that something's proper form comes to be in a way that depends on the form of another thing. So in exemplar causation we have two formal causes (that of the exemplar and the exemplate) and the existence of the one is made dependent on the other by the final cause; then the exemplar's form, although separate from the thing, works in a way as if it were the formal cause of the thing.
Exemplar causes are not the only kinds of extrinsic formal cause. I can think of at least two other major ones. Objective causes (which play a role in thought and in signs) are one; they differ from exemplar causes in that exemplar causes explain existence in some way, whereas objective causes complete cognitive and appetitive powers, and are causes of cognitive and appetitive actions being what they are. Another is a kind of causality that doesn't have a convenient name; perhaps we can call it a 'formant cause'. St. Albert noted in his study of mineral formation that 'place' was a cause that couldn't be neglected, and worked like an external form. That is, the boundaries of the surrounding medium contribute to how minerals grow and transform. Molds, like cookie-cutters or the kinds of molds used in arts and crafts and factories, are another sort of cause in this way; they affect the form of something by imposing a direct boundary during its formation. Exemplar causes, on the other hand, are causes of a thing as existing.
Suarez famously did not like this classification of exemplar causes as extrinsic formal causes; as he put it, the efficient cause also has a form on which the form of the effect depends. Thus he held that it was just a species of efficient cause. this is certainly not correct, because unless the efficient cause is itself the exemplar cause, the exemplar cause does not act, but is that according to which something is conformed. Part of the reason, too, that Suarez can get away with this is that he rejects the idea that extrinsic exemplar causes are really exemplar causes, so for him, exemplar causes are always internal to a mind. A view in which a live model is not an exemplar for the painting, or that a blueprint is not an exemplar cause for a machine built according to it, seems a very defective view. And it makes much more sense for us to take these 'external exemplar causes' to be to the 'internal exemplar causes' in something like the way that instrumental signs are to formal signs in objective causes, or instruments are to principal efficient causes. That is, they are 'exemplate exemplars' like instruments are moved movers.
It is true, of course, that an efficient cause always has a form, and that the effect depends on the action of the efficient cause, and the the efficient cause acts because of its form. And this is indeed just what efficient causation is. But the exemplar cause is, as the descriptions of it say, not the form out of which the agent acts but the form with respect to which the effect is formed. These can sometimes be the same, when the agent is also the exemplar, but they aren't necessarily so, and even when they are the same, the agent's being an agent and its being an exemplar are distinct. Some neoscholastic authors attempted to get around this by arguing that the exemplar is a 'moral efficient cause', and presumably an assisting one rather than a principal one, but this seems digging the hole deeper.
In the late medieval and Baroque periods, the exemplar cause and the final cause shared a similar fate; accounts of them increasingly relegated them to being things in the mind. Suarez in fact draws this conclusion explicitly for exemplar causes: he claims that they are only found in intellectual agents. But they are not merely things in the mind, although minds have very special and (for us) very important kinds of them (namely, purposes for final causes and design-plans for exemplar causes).
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* Our use of the 'idea' to mean (roughly) something definite in the mind is due in great measure to Descartes, who is explicit that he is adapting the traditional notion of 'idea' to his own use. It is very indirect, but Descartes's usage is actually influenced by Suarez's restriction of the exemplar cause, noted below.