Not sure of the details here, but it seems the Navy chief wanted to discipline Gallagher at all costs and was offering Trump to allow Gallagher to keep his Trident but take some form of punishment. Unfortunately for the Navy chief, he lied to his boss, SECDEF, about it all.
Your use of Navy Chief is incorrect language. What you mean is Secretary of the Navy.
I am pretty sure that Gallagher is in fact the Navy Chief, Chief Petty Officer
The navy is strange. Maybe this guy caught something exotic at Pattiya Beach?