Yes, in fact, people in their seventies may qualify to buy either term life, permanent life, or guaranteed issue life insurance coverage.
If you need guaranteed lifetime protection, then permanent insurance is a good option for you.
If you need the cheapest life insurance for a period of 20 years or less, then term life insurance may be a good option.
If you have health issues, or you have been turned down for coverage, you may want to consider guaranteed issue life insurance which offers guaranteed approval for seniors who meet the age requirements for acceptance.
Here's how you can get life insurance over 70 years of age.