Actually, it can go either way. It depends on how you diagram the sentence. I've been checking a number of grammar sites and they all agree that both usages are acceptable, with Americans tending towards the plural, treating "a variety of" as a modifier of "positions" rather than the reverse.
"...there is a variety of positions within Star Law..."
The subject of the sentence is "a variety of positions" in the context being discussed.
One could say "there are many/multiple" positions, where these modify "positions".
The alternative would be "there are varieties of positions", which would indicate that there are several distinct groups of positions of positions, which is somewhat ambiguous without qualifying context.
a variety of [n*]/[nn2] is 15/11 47/15
a variety of [n*]/[nn2] are 26/26 83/82
ratio plural:singular 1.7/2.4 1.8/5.5
For those unfamiliar with the query syntax, [n*] stands for any noun form, while [nn2] stands specifically for "plural common noun".
An important thing to note is that this has nothing to do with the verb immediately following the plural noun. We can move the verb directly in front of "a variety", but the preference for plural agreement doesn't change:
there is a variety of /[n*]/[nn2] 23/16/12 17/ 9/ 6
there are a variety of /[n*]/[nn2] 56/37/34 260/187/172
ratio plural:singular 2.4/2.3/2.8 15.3/20.8/28.7
In short, plural is the agreement of choice on both sides of the pond, though interestingly considerably more so in the US.
And as you pointed out yourself in comments elsewhere on this page, this is not really surprising, but in fact perfectly in line with how similar constructions such as a number, a lot, a total, etc. behave. This is sometimes referred to as notional agreement or notional concord:
As Quirk et al. 1985 explains it, notional agreement (called notional concord by Quirk and others) is agreement of a verb with its subject or of a pronoun with its antedecent in accordance with the notion of number rather than with the presence of an overt grammatical marker for that notion. Another way to look at the matter is that of Roberts 1954, who explains that notional agreement is agreement based on meaning rather than form.
In Wikipedia, the corresponding entry is to be found under synesis:
Synesis [...] is effectively an agreement of words with the sense, instead of the morphosyntactic form. [...] Such use in English grammar is often called notional agreement (or notional concord), because the agreement is with the notion of what the noun means, rather than the strict grammatical form of the noun (the normative formal agreement). The term situational agreement is also found[.]
Notional agreement for collective nouns is very common in British English. It is less customary in American English, but may sometimes be found after phrases of the type "a collective noun of plural nouns", e.g.,
... a multitude of elements were intertwined. (New York Review of Books)
... the majority of all the shareholdings are in the hands of women. (Daedalus)
... a handful of bathers were bobbing about in the waves. (Philip Roth)