In my Collins COBUILD Advanced Learner’s Dictionary 5th Edition, they wrote:
en|gag|ing /ɪng’eɪdʒɪŋ/
[ADJ]
An engaging person or thing is pleasant, interesting, and entertaining.
…one of her most engaging and least known novels…
He was engaging company.
I wonder whether we should use ‘a’ before ‘engaging’ or not? Because I often see sentences like these:
She is a charming dancer.
He is a hard-working engineer.
Thank you.
In your examples, “person”, “dancer” and “engineer” are all singular countable nouns, so they require articles. This is not affected by the intervening adjectives “engaging”, “charming” and “hard-working”. For example, just as we say “She is a dancer”, we say “She is a charming dancer”, “She is a beautiful dancer”, and so on for any other adjective.
In “He was engaging company”, the noun “company” is uncountable, so an article is not required.