When you say Draft Card, do you mean a Selective Service Registration Card? If so, registration was still going on through April 1, 1975 and then again resumed in the 1980s. Also, while the draft had ended, draft lotteries still continued for a few years (presumably, just in case the draft was re-initiated).

The last draft call was on December 7, 1972, and the authority to induct expired on June 30, 1973. The date of the last drawing for the lottery was on March 12, 1975. Registration with the Selective Service System was suspended on April 1, 1975, and registrant processing was suspended on January 27, 1976. Registration was resumed in July 1980 for men born in 1960 and later, and is in effect to this present time. Men are required to register within 30 days of their 18th birthday.

Source: https://www.sss.gov/About/History-And-Records/lotter1