新規 and 新たな cannot be used as a predicate, and they cannot be used in comparative sentences, either.
pre-noun adjectival |
adverbial |
comparison |
predicate |
新しい計画 |
新しく計画する |
これより新しい計画 |
この計画は新しい |
新たな計画 |
新たに計画する |
❌これより新たな計画 |
❌この計画は新ただ |
新規(の)計画 |
新規に計画する |
❌これより新規な計画 |
❌この計画は新規だ |
新しい is a plain word, 新た is a bookish and a little dramatic word (∼ "brand-new"), and 新規 is a technical-sounding word. 新規 is not a word we commonly see in lyrics. 新たな夢 sounds more dramatic than 新しい夢, but 新規の夢 sounds simply odd.
As 新規 is a kango (Sino-Japanese word with on-readings), it's often used before another kango.
I may be wrong, but 新規 may tend to mean "first-time" rather than "new". 新規客 and 新しい客 can both refer to "first-time customer (who has never visited the store before)" and "new customer (e.g., 8th visitor of the day after the first 7)", but I feel 新規客 tends to refer to the former. There is even an expression ご新規さん. The same can be said for 新規感染 vs 新たな感染; both can refer to first-time infection and reinfection, but 新規感染 tends to refer to the former.