If you've watched the first two minutes of cinematics in Halo two remastered, Agent Locke speaks to Arbiter to try and get background on Chief. Chief went AWOL and they want to get him back. This means they don't want to kill him. He's just going to answer for going AWOL and Locke and his team are on the hunt for him. 

Prediction (not set in stone, just a prediction): 

When Locke finds Chief they will have already gone so far down a a rabbit hole that the UNSC cannot understand. Chief was essentially upgraded by the Librarian so now he's been sped up a bit on the evolutionary scale, which is how he survived the Didact. This will make it hard for Locke and his team to take him down. He'll confide in locke though and if locke turns on him arbiter will get involved and all three will have to face the latest threat Chief was forced to go after to save universe. 

What do you think will happen?

I actually think Locke sees Master Chief as a threat to humanity, a view that formed during his time at Oni. remember, the spartans were never supposed to fight the Covenant, but rather human rebels. Master Chief never saved earh and humanity for humans, for him it was just another fight. Atleast that is how I think Locke sees him.

I do think we will see him gradually view Master Chief in a new light during H5 or H6, and I am interested to see what happened with the didact.

Yep. Something tells me the Didact isn't dead.