In modern English we expect “at the head of the government”. Elsewhere in the text we find two other occurrences of “head of ... government”, and in one of these cases there is no determiner:
In fact, this second example is precisely the same prepositional expression as here in Helaman 3:23 (“at the head of government”). Even though the original manuscript does not exist for either Helaman 3:23 or Helaman 7:5, their agreement strongly suggests that nothing is wrong with not having the before government in this Book of Mormon expression. The 1953 RLDS edition added the expected the here in Helaman 3:23, but not in Helaman 7:5 (which suggests that the addition was unintended). This error probably occurred because in English the word government usually takes the definite article the (for instance, there are 13 occurrences of the government in the original Book of Mormon text).
Summary: Accept in Helaman 3:23 and Helaman 7:5 the phraseology “at the head of government”; that is, without the expected the before government.