1 Corinthians 15:25 says:

"For He must reign until He has put all His enemies under His feet."

That wasn't a distant future event. It was happening in Paul's own time:

Hebrews 10:12-13 says,

"But He, having offered one sacrifice for sins for all time, sat down at the right hand of God, waiting from that time onward until His enemies are made a footstool for His feet."

(Written before 70 AD, stating the process was underway.)

Colossians 2:15 says,

"When He had disarmed the rulers and authorities, He made a public display of them, having triumphed over them through Him."

The powers had already been defeated.

Ephesians 1:20-22 says Christ is already seated above all rule and authority,

"and He put all things in subjection under His feet."

The last enemy was death (1 Corinthians 15:26). That was not biological death, but the spiritual separation caused by sin under the Law (Romans 7:9-11). That death was defeated at the resurrection of the saints in AD 70, when Christ brought full covenantal redemption and the old world fully passed away (Revelation 20:14, 21:1).

So yes, Christ completed His reign and put all enemies under His feet, just as promised.