Bit of a bizarre suicide-by-cop situation, but I wouldn't have indulged him and don't really see the point in doing so.
If you don't give Tarry the firing he wants, his most logical move would be to escalate. Give even more interviews, make up more policy and escalate attacks on the party for not backing the strikes.
At that point Starmer has to fire him, if he wants to keep any credibility. Which gives you the same result just with a bigger more drawn out story.
There is no good solution. Firing Tarry and getting it over with seems the least damaging.