In a firstorder logic, L, it is possible to transform a sentence, S, containing variables into a sentence S' in socalled 'clause form'  i.e. with a matrix in conjunctive normal form and a prefix consisting of only universal quantifiers  such that S is valid iff S' is. If L is expanded to a secondorder language containing variables and quantifiers ranging over firstorder predicates, but with no higherorder predicates (i.e. none that take firstorder predicates as their arguments) is it still the case that sentences of the expanded language can always be put into clause form in a way that preserves validity?

First, if you don’t place any restrictions on the transformation, you can actually make $S'$ as simple as you want in any logic: if $S$ is valid, let $S'$ be any fixed tautology, otherwise let $S'$ be a fixed nontautology. In order to rule out such a trivial answer, I will henceforth assume that the transformation $S\mapsto S'$ is required to be computable. Second, it’s stated wrongly in the question. In firstorder logic, you can introduce Skolem functions to make any sentence universal, but this transformation does not preserve validity, it preserves satisfiability. If you want to make $S'$ valid iff $S$ is, you need the dual transformation: introduce Herbrand functions to make the sentence existential. In secondorder logic, preserving validity, you can transform any sentence into a block of existential secondorder quantifiers, followed by a block of firstorder universal quantifiers, followed by an open matrix (say, in CNF). I’ll write this as $\exists^{SO}\forall^{FO}$. This relies on having secondorder function variables; if you only allow secondorder predicate variables, you need $\exists ^{SO}\forall^{FO}\exists^{FO}$. Dually, while preserving satisfiability, you can make any sentence $\forall^{SO}\exists^{FO}$ using function variables, or $\forall^{SO}\exists^{FO}\forall^{FO}$ using predicate variables. The basic idea is as follows (I will state it for satisfiability, as it is more intuitive that way). Secondorder quantification over a model $M$ can be simulated by firstorder quantification over something like $(M,\mathcal P(M))$. So, introduce predicates $M,P,E$, and include in $S'$ the sentence $$\tag{$*$}\forall X\,\exists u\,(P(u)\land\forall x\,(M(x)\to(x\in X\leftrightarrow E(x,u)))).$$ Elements satisfying $M(x)$ will represent elements of the original model $M$, and elements satisfying $P(u)$ will represents all subsets of $M$. Similarly, you can introduce predicates and axioms similar to $(*)$ simulating $\mathcal P(M^n )$ whenever an $n$ary predicate variable appears in $S$, and similarly for function variables. Then you can rewrite $S$ as a firstorder formula quantifying over elements satisfying these extra predicates instead of secondorder quantification. The crucial thing is that $(*)$ has only universal secondorder quantifiers followed by a firstorder formula, so in this way, you can transform any sentence into $\forall^{SO}\exists^{FO}\forall^{FO}\cdots \exists^{FO}\forall^{FO}$. Using Herbrand functions, any firstorder formula is equivalent to a $\forall^{SO}\exists^{FO}$ formula, where the secondorder quantifiers quantify over the Herbrand functions. This makes $S'$ into $\forall^{SO}\exists^{FO}$. The secondorder function variables introduced in the last step can be replaced by predicate variables ranging over their graphs if necessary, but then you need extra firstorder quantifiers to express that these predicates are really graphs of functions and to extract their value; it is possible to do this within $\forall^{SO}\exists^{FO}\forall^{FO}$. 

