Yes, but it depends on the type of life insurance, your health, and the insurance company age requirements which may vary by carrier.
Many term life policies have a maximum age limit to buy a policy of 75 or 80.
However, since permanent life insurance stays in force your entire lifetime, and the premiums are much higher, you may be able to purchase coverage up to age 85.
Here's an article for more information: Does life insurance have an age limit?