'The team captain' would also be correct. Although it is more helpful to think of this phrase as meaning 'Captain of the team ' because most times you use ' of the ' in English this will require the use of the genitive in Irish i.e. The name ' of the ' street, The colour ' of the ' car or The top ' of the ' pen.
@Fergall, Yes. Technically it is "the", but in English, in this case, 'the' is not needed.
He is the captain of the team = he is team captain = he is the team captain = he is captain of the team.
The thing it is never is anything meaning 'a team captain' or 'a captain of the/a team'.
For the latter, or if you wanted to emphasize 'the', yoy would need to use other constructions...