I read it in the context given as hyperbole, that he was clenching his jaw determinedly for quite some time.
This is Lexico verb definition 4.4:
with reference to a person's face) assume or cause to assume a fixed or rigid expression.
- ‘When he glanced back at the corner, jaw setting, she laid her hand on his arm.’
- ‘Following my faint shadow across the tan carpet and up to my feet then leisurely climbing to my face until our eyes meet, the enemy noticeably tenses and her jaw sets.’
- ‘His jaw sets and he doesn't respond, and I know he knows that was a mean thing for him to say, but I also know he isn't going to apologise.’
- ‘Their face tightens immediately; their features fall, the jaw sets and the arms cross.’
Alternatively, it's the adjective definition 1.2 — both are close in meaning:
(of a person's expression) held for an unnaturally long time without changing, typically as a reflection of determination.