You need not worry, since your original tourist visa is now void since you have departed New Zealand and returned home.
You are taking the correct steps in applying for a business visitor visa, since the nature of your next trip is for business purposes.
Just keep in mind the requirements for such a visa. According to the NZ Immigration official website for business visitor visas:
Visitors coming to New Zealand for less than 3 months
may be granted a Business Visitor Visa for any of the following
- to carry out an official trade mission recognised by the New Zealand government
- to sell goods and services in New Zealand
- to buy New Zealand goods and services
- to negotiate or discuss the set-up, expansion or wind-up of a business in New Zealand
- to carry out any business with the authorised representatives of an overseas company, body or person.
- To carry out any other work activities, or stay longer than 3 months, you'll need to apply for a work visa.
To answer your question:
Can I enter New Zealand again after receiving a tourist visa last March?
Yes, you can re-enter New Zealand on new (business visitor) visa. The 9 month stay limit is only for tourist visas, while the business visitor visa allows only 3 month stay limit. These are different visas with different rules. Luckily, you have stayed within the rules on your tourist visa, and are eligible for future visas in NZ.