"I ordered a Hawaiian plate for myself."
Translation:Ua ʻoka au i pā mea ʻai Hawaiʻi naʻu.
The Hawaiian word he is not commonly found in the middle of a sentence, especially after the word i. You could put ke before pā but that really would mean that you are ordering THE plate lunch instead of a plate lunch. Nevertheless, definite articles can be used in Hawaiian at times when in English we would use indefinite articles.
This lack of an article is a nuance of the language in this case when a request is expressed for an indefinite thing (a something).
In your sentence and in Chasavaqe's question, the i before pā is the indefinite article (a/an) as Kelii says above. The only thing I would add is that there is a 3 part rule that says when to use which form of a/an but I would have to dig to find it and Im crunched for time to make my daily goal right now.
Here's my take on this. 2 example sentences that mean the same. 1) "Makemake au I kekahi puke. I want a book. 2) "Makemake au I puke. I want a book. Reference:Olelo Oiwi Pages 120 and 121. This will clarify why there is no "He" in the sentence and why no "Ka" after the I Just my take on this. Aloha Kakou