Hans, head of a company that manufactures garden furniture, is announcing to his staff ....
Shouldn't it be the head of a company ...? Is that correct? Could you explain why we do not need a definite article here?
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Certain phrases that function like titles can be used without the definite article in certain contexts. See Araucaria's answer to Why “be king”, not “be a king”?
This usage is most commonly encountered in predicative contexts (e.g. "He is president/President of the United States"), but it can also be found in appositives, as in your question. I suppose this could be explained in terms of the "whiz-deletion" analysis of appositive NPs: "Hans, head of a company that manufactures garden furniture" could be seen as being derived at some level from the longer phrase "Hans, who is head of a company that manufactures garden furniture".
BillJ left a series of comments suggesting that "head of a company that manufactures garden furniture" should not be called an "appositive" because it does not work as a substitute for the subject "Hans". According to BillJ, it should be called a "supplementary NP" instead.
BillJ's comments seem to be based on some particular analysis/definition of "apposition" (summed up by the statement "An appositive NP must be capable of replacing the entire matrix NP"), but I don't know exactly what literature would discuss the arguments for using this definition/analysis. There seems to have been some debate about the syntax of appositives and related structures; Shoe left a helpful comment linking to a related discussion beneath this answer.
One article that seems relevant, but that I haven't been able to read yet, is "Nominal Apposition", by N. Burton-Roberts, 1975. From what I gather, Burton-Roberts reserves the term "appositive" for things that aren't derived from reduced relative clauses.
There may also be relevant information in "Appositional constructions", a 2011 thesis by Herman Heringa. I haven't finished reading it, but from what I've read so far, it looks like analyses that treat appositives as a type of reduced relative clause are not dead yet: Heringa says
O’Connor (2008) [...] argues that appositions underlyingly are non-restrictive relatives with a null relative pronoun as its subject.
Heringa also discusses things that he calls "appositions" that lack an article (the examples are taken from Dutch, not English, but seem analogous to your example) on p. 78, and mentions that Doron, E. (1994) ‘The discourse function of appositives’ uses examples like this as part of an argument that "appositions behave as nominal predicates" (p. 76).
Whatever you call it, the structure in your quote is grammatical.