The Time Patrol In 2022

In 2022, would the Time Patrol be working hard to maintain:

the irreversible climate catastrophe;

the British cost of living crisis;

COVID;

the war in Ukraine;

conflict in the Middle East;

other problems?

Not necessarily. Those problems do not necessarily exist in their timeline. Poul Anderson's account of Manse Everard's career came to an end in 1990, thirty two years ago. Whatever happens after that in their timeline is only what could have been projected or imagined by Anderson at the time when he was writing "Death and the Knight." 

However, we do know that the Time Patrol guards a history full of future conflicts:

the Martian war of 3890;

raids from Venus in the thirtieth century;

the Second Asteroid War in the twenty ninth or thirtieth century;

the Exaltationist rebellion in the thirty first millennium;

time travel bandits in the two hundred and fifth millennium.