Problem with male colleague not doing what asked

It isn’t sexism to use the correct pronoun for the specific person you are referring to! FFS, is this the reason so many people fall over themselves to “they” everyone these days?!

First, you can't manage him, you can only take this to your managers.

You have some evidence of his behaviour. You perhaps need more. Ask him in your next email to perform the another task, including deadline, documentation and deliverables.

If he has any issues with doing the task itself as it's set out, then he should direct his query to his manager. If he needs more details of what's required, he should ask you.

If he doesn't perform the task to your satisfaction, or makes decisions that are not his to make, you take it to your manager with your documentation. Be as calm and professional as possible. It's up to his manager and your manager to sort this out.

Don't discuss other peoples' issues with him - they will know - and it might make it sound personal.

If it was me, I'd put in a call with him. I wouldn't attack him personally but I'd say something like "I'm concerned we're seeing safety breeches in your department and know the consequences can be xyz. Can we come up with a plan to address this?"

If this doesn't work I'd then involve your manager but I do find bringing in the higher ups too soon creates more animosity.

Put it on him/collaborative session to come up with a plan.

Out of interest, did he apply for (and fail to get) your job?

Agree with practically everyone else about keeping records of everything and escalating to your boss if necessary, but if you do make sure you mention how well it's going with the other 4 sections first
If the boss is competent they'll already know this, but the guy will probably push back by insisting you're the issue and that's best anticipated and cut off

Go through your manager who can liaise with his manager

Absolutely ignore this. You are not coming across as arrogant at all.

I'd love to hear his side of this, you are coming across as rather arrogant yourself and I wonder if your manner of writing winds him up. If he is doing something against policy, record it. His attractiveness, relationship with other colleagues, or his "type" is nothing to do with the functions of the job.

I work in safety.

If someone, like your colleague, doesn't do what is required I raise with THEIR manager. It's for them to manage.

Personally I don't go to my manager as I wouldn't expect them to step in unless the other manager didn't resolve appropriately.

Document everything, keep raising it with your line manager in writing. They should be raising any failures to follow procedures to his line manager, which should then lead to a PIP, or possibly a disciplinary.

If your line manager isn’t taking this seriously then you have a problem.

Let your manager know every time. Then they will need to speak to him or his manager to get him in line. Don’t take it personally, it him not you.

Would Your line manager object to being cc’d into all your communication with him? I would ask for this too going forward.

It's not sexist to accurately reference someone's sex.

You seem to think this is about you as opposed to the fact he's been there for ten years and presumes (probably incorrectly) that he knows what he's doing.

So his looks etc and you not fancying him is irrelevant, just whether he's doing what he should be doing is the big thing and that's something you can simply document and make sure it's clear you're doing everything you should be doing.

If it hasn’t been recorded, it hasn’t been done

It seems he thinks that he thinks what he does in his department is just his decisions and what our department asks (or just me) he will not do. My department has say over every department because we ultimately keep others safe

Just on this bit - I would first double check that you ARE officially able to 'task him' to do things.

I've been on the other side of this coin...constant emails from x instructing me to do xyz when in fact they had no business contacting me directly to do anything. I had my own caseload, my own responsibilities - and just because their department (risk/compliance) had overall oversight of my department, it still didn't mean I was their lackey to carry out tasks for them. It turned out that they were the one that had misinterpreted their reach and level of authority, not me, and it resulted in an extremely embarrassing meeting (for them).

This will ultimately be your bosses responsibility if things go wrong.
Make it clear to your boss that your sole concern at "them" not following safety procedures is that it exposes your boss.
Tell your boss you will be reporting every single breach so that he is fully informed and you will be covering your arse.
Cc your boss into all futher queries.
Confirm all conversations by email too.
Tedious and a PITA but what you have to do to cover yourself.

I would say not only email your manager, but carefully choose your words when you do so - don't say "he did this" but use the more gender-neutral form of "they did this, they didn't do that". Protect yourself against anybody calling you out as being sexist.

I would report to compliance. He poses a risk.

Unless HE is compliance in which case I don't know!

If it's safety critical whoever has ultimate safety responsibility should be chasing. And above your head I would report it so that your arse is covered. If people ignore it you have still done the right thing.